Removing old flush mount marine speakers is not too difficult. The first step is to remove the mounting screws. On some models the screws will be obvious and easy to get to. Other speakers have a snap-on grill that hides the screws. You will need to snap-off the grill to reveal the screws. Usually this can be done with hand pressure, but sometimes a small screwdriver will help give you the leverage you need to pop it off.
Remove the screws with a screw driver and the speaker will become loose in it's position. You will want to be careful though, because the speaker is still attached to the wire. If it drops from position, it might yank on the speaker wire and damage it. Slide the speaker out and then remove the speaker wire from the positive and negative terminals on the back. There may be tabs that attach the wire to the terminals and these will usually just slide right off. It's also possible that the wire is soldered to the terminals. If this is the case, you might be better off just snipping the wires close to the terminals.
Once you have detached the speaker wires you are done! You may want to tape the wires temporarily in place so that you don't lose them behind the mounting surface before you can put in your new speakers.