Was there a recall on the door handle plates on the 2005 H2?
Not that I have heard, I would call the dealer and give them you VIN, they will be able to tell you. The US site to check for yourself is: http://www.nhtsa.dot.gov/ The Canadain site is http://www.tc.gc.ca/roadsafety/recalls/search_e.asp best of luck.
Search Hummer H2 Questions
Hummer H2 Experts