My girlfriends ex-roomate wants her cat back (Ohio)

On July 24th of this year, my girlfriends ex-roomate moved from Ohio to New Hampshire to work temporarily for 3 months. Her roomate got the cat from a friend, and had it spayed. The roomate asked my girlfriend to take care of her cat while she was away, her exact wording was to take care of the cat until "no later than October". In this time, my girlfriend has grown very attached to the cat. She has registered her as her emotional support animal (with all documentation from her doctor), and has paid for food and litter the entire time. Her ex-roomate is coming back on November 5th (4 days from now), and the assumption is that she will want the cat back, although she has not reached out to my girlfriend stating her intent. Does my girlfriend have to give the cat back? Is there any law requiring her to give the cat back? Her ex-roomate does not yet have a living situation figured out for whenever she does get back either. Is there anything that we can do?