Professor Recommendation quick question?

So I told my professors I’m applying to NYU as a transfer student and asked if they could write a recommendation for me. The problem is that I’m applying to another university as well and assigning them as recommenders on common app. I didn’t mention the other university so now i’m like "Crap what if they write “this student is sutiable for nyu…” and the other university sees this :((?

Does anyone know what would happen? Would the other university be weirded out and all, and not consider me as seriously :(?

Tell them now to edit the name out of the university and upload a neutral letter.

I spoke to an admin. Officer from UPENN and she said that a lot of times, students use the wrong college name in their personal essays. They app readers dont really mind because they realize that its just a simple mistake, though it would be better if it didnt happen.