My daughter pushed in a tweeter when she was very young and I was incredibly annoyed by the incident. In all honestly I never could hear the difference in sound with the tweeter being pushed in, but it bothered me - they were Dynaudio. I eventually sold them once at a huge discount to family friends who just wanted nice sounding speakers. They were extremely pleased with their sound and just left the grills on. They still have them this day and when I go to their house I am still impressed by their sound quality driven by a mid-fi amp.
Unfortunately I do not have good advice - I tried several methods and though the tweeter came back out, the tweeter manifested wrinkles.
On a side note - I went to my friends house recently who has mid-fi speakers. I noticed his tweeters and mid's pushed in. When I asked him what happened he told me his wife who hates dust pushed them in while dusting. He replaced them and leaves the grills on his new speakers. They are still happily married.