What about an art gallery that gives away free souvenir prints of their favorite works, and when you get home you draw silly mustaches on your own copy? I think that's more like what's happening here.
I agree, but what if you draw the silly mustaches on the paintings and hand them out without telling anyone that the silly mustaches were added on by you? ...
The same answer applies to both.
In many cases the copyrights to the artwork in a museum have
expired.
If not, the artist can sell his copyrights to the museum. In most
cases where copyright has not expired I would guess, and it is only
a guess, that the artists have licensed the museum to make and
distribute the copies.
It is unlikely they have done the same to the mustache drawers.