As for the convex on the speaker then ...
NOT! Do not stab the membrane with needles! It is better for it and 100% effective!
Dampen this protrusion with some deodorant (NOT WATER!) In a sprat - it should be moist. Turn on the vacuum cleaner, reduce its power to a minimum (if possible), open this window on the suction pipe - the point is that the vacuum cleaner should have as little draft as possible!
When you start with a high thrust, goodbye to the speaker - it will tear the diaphragm out of the basket! Yes "regulated" vacuum cleaner
turn off . Put the end of the pipe to this lid and turn on the vacuum cleaner.
Once again:
On the lightest thrust !!! Hold the end of the pulling vacuum cleaner for a few seconds and turn it off
without taking the pipe off the lid! If you tear off the pipe during the draft - you will tear the membrane

When the vacuum cleaner stops - remove the end of the pipe from the membrane and see what it did. If not much, repeat it
SLIGHTLY increasing the thrust of the vacuum cleaner. After a few tries, your speaker is like new. Let the membrane dry (several dozen minutes) and enjoy the repaired speaker.
I don't take responsibility for what you do with it! In this way, I have already repaired the mass of the speakers. This method is not suitable for tweeters!