Can colleges check AIME/AMC Scores?

I am an AIME qualifier; however, I cannot remember my score (it was either a 5 or a 6). Do top colleges like Princeton or MIT routinely check (if they’re even able to) their applicants’ AIME or AMC scores?

I’m pretty sure if you want to use it on the MIT app they ask for the score.

You don’t have to report AMC or AIME scores (though it’s a good idea if you score well), though I don’t know if they always verify the score. Of course if I put down that I got a 15 on the AIME, then they might check that, and if I put 16, then they’ll probably call BS.

Is there a way you can contact your school (or whichever organization you took the AIME with) to see if you can view your score report?