I would be more worried about how to remove that aiptasia.
But to answer your question, I have had luck getting under the base with a very small flathead screwdriver, the kind used to fix glasses. Just take your time and start peeling up the base, try to remove it in a single piece. Leaving a fragment behind will produce another mushroom.
Best to attempt this method before the lights come one, that way the shroom is mostly retracted. GL