RayV wrote:
Get one of those stick on drywall patches, paint over it and mount the
old towel rack to a stud. The towel hanging on the rack will disguise
the patch next to it.

I also recently used this yellow, mesh tape for the first time. It was
great for holes that were about the size you said yours is. I think
they recommend making a plus (+) with two pieces of the tape and then
mud over it like you would over one of those sticky patches that RayV
suggested.

Ryan