You can see the replacement tweeter here:
https://www.madisoundspeakerstore.com/soft-dome-tweeters-hivi/hi-vi-tn28-top-mount-1-fabric-dome-tweeter/
I can't get to the tweeter though as there's this cover in the way. You can see the cover in the first pic you posted.
I have found out it is a dovetail shoe mounting. Only the base screws.
Disconnect the wires from the crossover. See if you can insert a thin blade between the tweeter and the base and slide it forward.
If all else fails that tweeter is no good. I would give it a good clout on the rear with a heavy soft hammer. This should move it forward.
You can then slide in the new tweeter. Be careful not to crimp the wires though.
If you do end up damaging the base, then you can mount the new one from the top with long bolts and place washers and buts inside the cabinet.
They must have mounted the base and then glued on the top, to make things difficult.
You are going to have to use some brute force most likely, as apparently these units really bind in the dovetail shoe of the base.