I've read quite a bit about the Temple Mount Faithful, and I don't believe that they themselves are planning to do anything to the mosque. I was under the impression that they believed G-d Himself would take appropriate action. ;-)
Actually, they believe He is already taking action! Go to Temple Mount Faithful and read about the "cracks" and "bulges" on the wall... They believe the Lord is ready to act, since His people won't, and they are getting ready for the day it happens.