We hired a Yeshivah dining hall for an event. One of my teenage boys threw a plastic chair which broke. I did not approach the Rosh Yeshivah since he already suspected my kids of causing some other damage (which was not the case) and I do not want to cause further ill feelings. The Yeshivah has a lot of these chairs so they are not lacking the chair that was broken. Could I make an anonymous donation to the Yeshivah in order to cover the damage.
Provided that you are certain the yeshiva won’t suffer any loss beyond the monetary damage, there is no problem in paying back the money as you suggest. Of course, you have to ensure that the amount you contribute covers the cost of the chair.
In addition, the donation should be given anonymously, so that the yeshiva won’t be under the impression that you are giving a regular donation.
Best wishes, and sorry for delay in replying.
See Choshen Mishpat 355:1-2; there is no essential problem in paying back without the other party’s knowledge, and the problems discussed in the Gemara (Bava Kama 118) and the Shulchan Aruch are side issues related to animals and to the guardianship of items.