I don't see any traces on the topside of the board, so it looks like a singled sided board. Should be easy-peasy to pop that thing out. You'll want a solder sucker to do that. Medium tip? I usually use a small one to do most work, but here a bit larger than pencil would work better, more heat transfer.
You could do it with solder wick but eh, sucker is the way to go.
I do think the transformer is junk and assuming it's not $50 I would be swapping it out. Anyhow, I don't blame you if you want to source that out, I wouldn't say soldering is hard, but it is a skill to be learned, and if you're not going to use it again, well... I know friends will hit me up for soldering work. [Some day I might go get trained, we talk about it at work from time to time.]
You could do it with solder wick but eh, sucker is the way to go.
I do think the transformer is junk and assuming it's not $50 I would be swapping it out. Anyhow, I don't blame you if you want to source that out, I wouldn't say soldering is hard, but it is a skill to be learned, and if you're not going to use it again, well... I know friends will hit me up for soldering work. [Some day I might go get trained, we talk about it at work from time to time.]