There's no need to assume. I searched the US trademark database. There was a registration for GIMP in 2001, number 78084356 ("computer programs for creating and manipulating graphic images on a computer. FIRST USE: 19990600. FIRST USE IN COMMERCE: 19990600"), but it's abandoned since June 7, 2002. There are no other relevant registrations that I can find.
As far as I can tell, there's no formal "GIMP organization".
True, although http://www.gimp.org/donating/ states that "The GNOME Foundation has graciously agreed to act as fiscal agents for us." Maybe they could hold the GIMP trademark?
By the way, the trademark you mention was Caughron, Mathew K. INDIVIDUAL UNITED STATES, who seems to have been responsible for the old WinGIMP and MacGIMP distributions that cost money.
As far as I can tell, there's no formal "GIMP organization".