The short answer, I suspect, is that it belongs to whoever wants it.
I worked at hotels as a teenager. The bibles are sent to hotels for free by the Gideons (or, in some cases, some other religious organization). We used to have boxes and boxes of them in the basement. A Gideon representative would come around every year or two to make sure there were enough.
I guess technically they belong to the hotel; but since they are provided en masse for free, I can't imagine that the hotel would really feel much ownership interest in them.
I think the "I'm not a Christian and I don't want to have this in my room, will you please come and remove it" line would almost certainly work.