The Shulchan Aruch (C.M. 359) writes:
אסור לגזול או לעשוק אפילו כל שהוא בין מישראל בין מעכו"ם.
ואם הוא דבר דליכא מאן דקפיד ביה שרי, כגון ליטול מהחבילה או מהגדר לחצוץ
בו שיניו. ואף זה אוסר בירושלמי ממדת חסידות:
It’s forbidden to steal or exploit (even) any amount, whether from a
Jew or a non-Jew; And if it is an object that is not concerning, it is
permitted; such as to take [a straw] from a package or [taking a splinter]
from the fence to brush his teeth with; and even this is prohibited by
the Jeruselamite (Talmud), as a quality of fervency.
The Sema explains the reason to not allow taking even a negligible amount:
ואף זה אוסר בירושלמי הטעם כתב הנ"י דאלו עושה כן כל אחד נמצא החבילה כלה והגדר נהרס עכ"ל:
The reason is, writes the Nemukei Yosef, if everyone would do this, the package would be exhausted and the fence would be ruined.
So, in this case, if the university would never be bothered by the amount of disposable utensils being taken, it is strictly speaking permissible, but recommended not to take any (more than the expected one for that meal, of course). A larger amount (10 at once) that is not necessarily overlooked is forbidden. This is true even if in the particular case the university doesn't care, so long as it is an amount that they might reasonably be strict about (three maybe?); until receiving clear permission. (BTW, the person behind the counter might not be the one who can give permission.)