I put mine under my tallis bag until the end of davening or until I can get to the back of shul to throw it out in the garbage can.
I also find it quite disgusting (for lack of a better word) for mispalelim to leave it on the table to have it glaring me in the fase during davening and many times “forget” to take it out after davening.
Yasher Koach for bringing it up L’Ma’an Kedushas Beis Hakneses.