How big an area does it cover and have you tried digging it all out (not a daft question as you don't indicate the size of the problem) Are there plants you still value surviving underneath it - this could affect the solution.

Most Geraniums, unless only recently planted and still fairly small, cannot be 'pulled' out, you need a large fork or spade to do the job and get the roots out. G. Johnson's Blue, in particular, has quite deep roots that go down two spade's depths, so its likely that other varieties are similar.

I agree, digging it out and getting all the root is the only way. It's a losing battle in my garden!