If their range and precision allow, they can teleport on the opposite side of the Earth (the height will influence air pressure: teleport ten kilometers too far, and you'll find yourself in the stratosphere, and die of pressure shock, cold and/or oxygen starvation). This way, gravity itself will act as a brake.
Otherwise they could teleport horizontally around the Earth, provided they can do so at a high enough rate that the build-up of normal velocity does not nullify the effort. Their speed will remain the same, but its direction will slowly vary in respect to the surface.
Actually, since their velocity (with respect to the center of the Earth) is about 200 km/h vertically, and 1000 km/h horizontally due to rotation, teleporting to a place about 30 degrees rotation-ward will transform a part of those horizontal 1000 km/h into an upward component, partially negating the descent speed. It should be possible (height control is still paramount, because of pressure/oxygen) to find the best distance by trial and error.
Something like this happens in Vernor Vinge's The Witling, even if the people involved are inside a capsule that is being teleported.
Update: actually, the "teleporting to the opposite side of the planet" will not work. This is a plot point in Vinge's novel: people able to reng (teleport) air from the opposite side of the world can make people here experience the airspeed of the opposite side of the world – and use this as a weapon. Teleporting and suffering an air blast at Mach 3 will be instantly lethal. Possibly, even the drag acceleration will be enough to make the teleporter lose consciousness, at which point they'll naturally fall down to their death.
Failing this, they need to shed velocity in some way. There are no safe ways of doing so; maybe the least bad option is to teleport above a lake. A terminal velocity impact on water is survivable, if harmful, if one has time enough to prepare (you need to achieve a high, but regular, deceleration). Also, terminal velocity (around 200 km/h, equivalent to a fall from a height of about 450 m) can be decreased even substantially, e.g. if one can arrange one's garments in the form of a funnel. Only in Hollywood movies could someone have the presence of spirit and speed for doing this, but our transporter could do this in stages. Possibly, transporting themselves fifty meters higher as soon as they feel the impact could spread the damage in two "installments", so to speak.
A very deep snowy incline would also work (there are reports of people falling from kilometer-more heights over snow and surviving. Vesna Vulovic famously survived a fall of more than 10 km after her airplane was destroyed by a bomb).
update: teleporting rotation-wards
TL;DR: it... could... work!!!
I have run some Geogebra simulations. When teleporting from point B to point C, separated by an $\alpha$ angle on the rotation plane, the two velocity vectors $u$ horizontal (due to rotation) and $v$ (due to the initial fall) remain unchanged, but their orientation relative to the surface changes their "meaning". In the new position, the fall is reduced to vector $b$, which is $v \cos \alpha$, diminished by the new "vertical" component of the rotational velocity, $a$, which is $u \sin \alpha$. So the new fall velocity is $(v \cos \alpha - u \sin \alpha)$.
For a terminal velocity of 200 km/h and rotational velocity of 1000 km/h, we want $200 \cos \alpha = 1000 \sin \alpha$, which means an $\alpha$ of $\arctan(0.2)$ will make the two components neutralize one another. I had estimated this to happen for an alpha of 30 degrees; it is actually 11.31 degrees, or a distance of about 1200 km (in the picture the two velocities are closer together, so it seems that the correct angle is double that).
What happens to the horizontal velocity when teleporting 11.31 degrees rotation-ward?
The new vector is the sum of vector $w$ and vector $d$, where $w$ is $v \sin \alpha$ and $d$ is $u \cos \alpha$.
This gives $200 \sin 11.31\unicode{xB0}$
plus $1000 \cos 11.31°$,
or $39.22 + 980.58$, or about 1020 km/h.
So after the "right" teleport our vertical velocity is completely neutralized and we find ourselves going up a wind of 20 km/h, which is tolerable (cue thunderclap).
This can also be done with about ten jumps towards the horizon (which at an altitude of 1 km is about 110 km distant); this is desirable because a visual check of the reentry altitude is better (if you rematerialize at a very different altitude, the difference in air pressure is likely to be nasty). Each jump will experience a slow-down in the fall speed and a slight head wind.
After this, shorter and faster jumps rotation-wards will pull the teleporter "up" and allow to fine-tune a safe descent.
In the case of terminal velocity, the time taken by the teleport is irrelevant, because during this time the fall speed does not increase (since it is "terminal"). So, the teleporter may refine their range by waiting each time until they've built terminal velocity, and then jump (to build terminal velocity, a fall of about 450 m is enough; it takes around 12-13 seconds).
But even if this were not the case, it would not be a great matter; all that would be needed is to take the extra speed into account (i.e. design the jump to neutralize not the current velocity but the one that will be reached at jump time, in, say, three more seconds).
On the other hand, this means that once they've stopped their vertical motion, they need to land very quickly before building up more speed. So they want to be, say, high above water; at that point they teleport straight down, as near the surface as they can.
honestly
Determine spinward direction (possibly by trial and error, making jumps with a small horizontal component and seeing what happens), then start making longer and longer (or faster and faster) jumps to and fro, in the direction where you feel wind at an angle of about 5° from the vertical. This wind will become less and less, and more and more far from the vertical, when approaching the "ideal jump". If the jump does not work, jump back to the original position, some distance higher, and retry. The horizontal component will not have changed much and will be soon compensated, and the vertical will have remained the same also, because you're falling at terminal velocity.
While doing such jumps, endeavor to reduce your altitude to take advantage of the denser air, and see if you can spot a suitable body of water. If none is found, teleport higher in the new position; soon you'll be falling at terminal velocity there too, and you can restart the whole process 1200 km to the east. At most after twenty such iterations you're bound to find water: at worst, the Pacific. Once you splash down, you can play human skipping rock going west, in shorter jumps, each time letting the water neutralize the small speed gained in the jump, until you are safely near a beach.
To further reduce speed you can try and get off e.g. the trousers or jacket and fashion a small parachute. The goal is to lower airspeed as much as possible, which allows shorter and more precise jumps.
cheating
Teleportation comes with a sense of matter – in the Vinge novel above, the Azhiri can "seng" around them and so have a "feel" for the volume of space they'll swap into. This sense, this instinct, also extends to speed – your teleporter can "feel" the relative tranquility of a given volume of space, and won't teleport onto a hurtling train. The discomfort sensation is greater the higher the speed differential.
Evaluation of a volume is then easy and instantaneous, in the same way that we can examine a vast area of space and immediately and effortlessly pinpoint the place with the highest photon reflectance in a given interval of energies – a task that would appear impossible to someone who had never heard about the sense of sight.
So, the teleporter keeps teleporting in places where the unease is just right, waiting for the sense of unease transmitted by the solid ground to abate; when this happens, they'll just teleport on the safe area on the ground they perceived.
The difficulty is then apparently enormous, but to a teleporter is no more difficult than it would be, for us, finding a suitable shade of green on a continuous thermal map, even if the map would change after each jump:
