I undid the screw on the back of it and the button that you gotta press down to change gear is still stuck. Am I doing something wrong? :(

There is no screw holding the button. It is held by clips.
Carefully prise out the button and withdraw the button and the spring. Noting the installed position of the spring seat, withdraw it from the handle.

Ref. Gregory's service&repair manual

All the screw does is hold the gear knob in position.

You need to slide a small flat screwdriver down the sides of the button and it'll pop out.

Okay, thanks guys.