I would say likely they want it back. Lots of folks don't realize unless they explicitly buy the modem it isn't theirs.
Sometimes they can be silly about it. You may remember way, way back that cable companies inched their way up to (I think) 30 channel systems . You couldn't get those channels on most TVs so the cable companies gave you a tuner box with a big knob that you used. The local cable company was purchased twice. The original company never bothered collecting the old worthless tuners because it would have cost them more than they were worth. The third owner decided it was going to make some extra money so it started mailing $125 bills out for the probably >20 year old worthless equipment that no one was likely to have. A family member got a bill. I went to battle with the cable company and kept on escalating it until finally they sent out a letter that essentially said "forget about it".