How do you remove the handbrake gaiter on an 87 X19?

Have a new rubber gaiter to fit on the handbrake of my 87 X19.How do you get the old one off?Don"t want to use brute force

As far as I remember its just pulled over the edge of a frame that's fixed to the transmission tunnel. The carpet can make it a bit awkward.
When I pulled the gator off over the handle I managed to move the hand grip up the lever without noticing. I could put the handbrake on but couldn't then push the button in. I was about the dismantle the whole handbrake system before I realised the cause

Many thanks for that.Followed advice and new leather gaiter fitted.Looks excellent