The Earth-people took all of their things and detonated some sort of nuclear weapon (?), which devastated the population and changed the landscape.
In order to maintain a significant amount of radioactivity after a few hundred years, you might consider salted bomb. These are specially modified nuclear devices which make use of the intense neutron flux generated by a nuclear explosion to transmute some material via neutron activation into some suitably dangerous, suitably long-lived radioisotope.
The most long-lived material considered was cobalt-60 which has a half-life of a bit over five and a quarter years, and therein lies the problem. A bit after 52 years, the radiation will have fallen to less than 0.1% of the starting level. A bit after 104 years, it'll be less than 0.0001% of the starting level.
You want something which is still dangerous after several hundred years. Radio-isotopes which are strongly radioactive lose their radioactivity more quickly. Long-lived radio-isotopes must necessarily be less radioactive. this means that you can't really create a salted bomb that produces dangerous radioactivity several hundred years after detonation. (edit: if you made a lot of salted bombs using nickel-62 cases you might be able to achieve your goal, see footnote)
Instead, what you probably require is something that's not merely a genocidal warcrime but also an instrument to carry your spite down the generations (or alternatively: deny an ecosystem to an opponent who might be capable of building closed life support systems and surviving in them for generational timescales... a trick a mature spacefaring civilization might reasonably have developed). This probably needs to be some kind of nuclear reactor, fuelled up ahead of time and built to operate unmaintained for many decades. It creates a steady supply of deadly radio-isotopes by a continuous process, using up a feedstock of suitably fertile material which can then be reduced to some suitable fine dust and blown into the atmosphere where high-altitude winds can carry it around the planet.
A number of these continuous fallout generators can be constructed and placed in hard-to-access bits of the planetary surface. Disabling the devices might be difficult, and blowing them up would be counterproductive as it could release more radiation in the short term. A clued-up spacefaring visitor would be able to detect elevated levels of radioactivity, identify the offending radio-isotopes, realize they must have an artificial source, and track wind patterns to track them down, and then see about sealing them off and shutting them down with robots.
Fictional spacefaring civilizations are notoriously unable to do this baby's-first-exoplanet-landing routine and will be breathing the air, drinking the water and investigating the orifices and intromissive facilities of the locals for biocompatibility before you can say "how have you people survived this long?".
I want a way to have these off-worlders experience some kind of sickness due to the high levels of radiation on the planet. Is this feasible to do?
Sure. Radiation sickness is depressingly well documented. How it would manifest (and how severe it would be) in non-human species is of course entirely up to you.
If you were interested, wikipedia has a list of radioisotopes sorted by their half-life... the mega and gigasecond decay times are probably the ones you're interested in. Long story short: there are almost no neutron activation products with the required half lives, but there are a few exotic fission products and cosmic ray spallation products that are impractical to produce on a large enough scale.
You're left with Nickel-63, with a half-life of about 100 years which can be made via neutron activation of stable Nickel-62. This is naturally stable, but uncommon on Earth (~3% abundance). Oak Ridge National Laboratory manufacture Nickel-63 from enriched nickel by irradiating it in a research reactor, using the result as a radiotracer. It may be possible to use Nickel-62 as the casing in a nuclear bomb for long-lived, lower-energy salted bomb fallout. It'd still have a quarter of its radioactivity after 200 years, but you'd need to make an awful lot of it to start with. Radioactive nickel is considered slightly less dangerous than some other forms of nuclear waste... notably, you have you ingest or inhale it. Compare with the ambient radiation risk of the high-energy gamma rays released by Cobalt-60. A death factory might be easier to build, and guarantees more radiation over a longer timescale, and that radiation will be continually released into the air instead of being trapped in soil and sediment.
