My rational guess is, the aliens would not brush their teeth.
There are several alternatives to "brushing teeth", including wiping them, scraping, hard rinsing (sometimes with a disinfectant or antibiotic), flossing and picking (e.g. using a toothpick).
Also for rinsing, frequent alcohol consumption can improve dental health; and that used to be extremely common amongst everybody (children included) when weak ale was consumed instead of water (water, contaminated by waste and refuse, made people sick: Weak ale, with about 1/4 the alcohol of modern beer, sterilized most of the bacteria, making it safer to drink: And better for the teeth.
Many of the things we do, we do out of cultural inheritance; brushing is likely one of those: We didn't brush for 99% of the last 50,000 years (when we suspect modern rational brains first appeared). (See here for the invention of the toothbrush in China, 1498).
We only began our current extreme hygiene and anti-smell rigor relatively recently; just a few centuries ago the idea that somebody had bad breath or bad body odor was seldom noticed: Everybody stank all the time! People bathed infrequently, and often not at all; they often wore perfumes and excess clothing to cover up their stink.
It is entirely possible for aliens the idea of sticking a tool in their mouth, like a toothbrush, spoon or fork, repellent: We have seen similar reactions in human culture. Although the Chinese did invent the first toothbrush; notice that the Chinese eating implements do not get as deep in the mouth as spoons and forks: chopsticks barely make it past the teeth, they are intended to just bring food to the mouth, not shove it in. The Chinese version of a spoon does not enter the mouth, either: it is more of a small bowl with a handle; it also only brings the food to the mouth, but the tool does not enter the mouth. It is plausible an alien race, even looking like us, could be repelled by the idea of putting anything but food into their mouths.
Toothbrushes only offer a slight mechanical advantage in cleaning the teeth and are not very thorough at all; it is why we are still encouraged to floss, and on top of that, need periodic cleaning to remove plaques. My point here is that brushing is obviously not the pinnacle in tooth cleaning, it is not the ideal approach, or the most efficient, or the most thorough.
I imagine there are dozens of other ways to partially clean teeth, to the same extent or better, to prevent cavities or disease. A disinfectant/antibiotic rinse (like with alcohol, spit out), combined with tooth picks and/or flossing for the stuck bits, seems the most obvious for teeth like we have. With dozens of alternative methods that can be just as successful, it seems unlikely we humans and the aliens would both arrive at the same flawed idea.