My daughter pushed my tweeter in-HELP!

Sticky tape. Be very careful and try several times increasing the contact area until you get just enough adhesion to pop it out but not too much that you damage it.

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.

Take the cardboard piece from inside a used up toilet paper or paper towel roll, put it up against the tweeter and gently suck it out yourself.

Igoler...a simple fix is by removing the front plate/diaphram.  Look at the front face plate of the tweeter, if the front flange has screws to hold the diaphragm to the motors then you can take the front plate of the tweeter out to access the diaphragm.  The front plate/diaphragm comes off, you can pop the sillk dome back out from the back.   

Sample Video on how to access the diaphragm from the tweeter.  

https://m.youtube.com/watch?v=9m92h83DhsA