Backyard drainage issue (inappropriately refilled pool)

[Haiyang A.]

I'm looking at a bank REO that needs some repair (only 20 years old), but it's the drainage issue in the backyard that worries me. The yard is on a slope, and it looks like that rain water would run towards the house (see 3rd image). However, the garage and the back of the house (including area underneath the deck) are pretty dry.

There is a very large area that is quite muddy with very noticeable green grass (growing like on a refilled swimming pool, see 2nd image). I thought about installing a French drain system to fix the drainage issue, but I worry that it’s a refilled swimming pool that has not been done correctly (e.g., not drilling enough holes at the bottom of the pool, and now causing this backyard marsh). If that is the case (how can I find that out?), then does that mean I need to excavate the swimming pool, get rid of the bottom part, redo the refilling, etc. I wonder how much would that be? Do I need a structural engineer to take a look at this, or would a lawn care person will do the job just fine?