Q. There is a bachur who placed his hat and jacket on a tree during Shabbos (or before Shabbos). Is there any heter to remove it from the tree on Shabbos to avoid the great embarrassment of davening without the proper attire that is worn by all bnei Torah when they stand before Hashem in prayer, and the embarrassment of appearing without the proper attire in front of great rabbis who are visiting the yeshiva’s camp? Kavod habriyos pushes aside a rabbinical restriction. Let us assume that it is not possible to borrow, or he is embarrassed. To note that if there would be a shofar on the tree on Rosh Hashanah, one could not remove it even though he will neglect a positive commandment of the Almighty, but perhaps this case is different.

A. Shulchan Aruch (O.H. 336: 13) and Mishna Berura (ibid. 59) rule that it is prohibited to hang or place anything on a tree on Shabbos. Our sages also prohibited using an item hanging or leaning on a tree, or placing articles on a branch as an extension of the prohibition.
Horav Shlomo Miller Shlit’a suggested to ask a Gentile, if available to remove the jacket from the tree, thus creating a shevus de-shevus or a double rabbinical prohibition permitted in need or for oneg Shabbos. (See question 753). It could similarly be removed while still ben-hashmoshos or twilight, before the beginning of Shabbos.
However, the Rov maintains that one may not remove the jacket even with a proper shinui, such as using the elbows or one’s shoulders, since the issue involved is not only a muktzeh prohibition, but also a g’zeirah for avoiding cutting parts of the tree if one would be permitted to use it.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a