I don’t have a "proper" talit bag but rather have been using a plastic bag from a pet store with a barely visible picture of a cat and dog. I do have a "proper" tefillin bag. The other day in the beit k’nesset, a worshipper (not a community member) told me that I "must" change the tallit bag because of the animal picture (After I remove my tallit, I place the bag on the seat of the chair next to me and do not see it when davening; obviously, the picture is not the object of my worship.) Is it forbidden to bring such a bag into the beit k’nesset? I’ve noticed parochets in Israel that have figures of lions on them representing the tribe of Yehuda - are these problematic also?
It might be more of a Hidur Mitzvah – beautifying the Mitzvah - if you use a specially made Talit bag yet if you don't have one, you can use any bag including a pet shop one.