please ID - sponge?

[c_scherer123]

I have a pest taking over several colonies of zoos. It is purple, and tends to throw out "shoots" which break off and find a new home. It spreads quickly, and is very invasive - it is even giving my 'island' of GSP a run for its money.
I think it may be some kind of sponge. It looks like it would tear away with ease - it is soft, but doesn't peel away easily, tearing and leaving you about .5 cm of stuff in the tweezers and leaving chunks behind which grow unhindered.
I remembered reading somewhere to avoid letting air touch sponges (at least ones you want to keep), but I gave my one zoo colony a 20min breather, without fazing the pest. I gave another a freshwater dip, and swirled it for about 30 sec, but it still didn't bother the pest.

What is it and how do I get rid of it?

The purple stuff between and below polyps isn't their base, it is the pest. You can see it weaving in and out of the GSP polyps