My wife and I moved into our house a little over a year ago and we are getting ready to make some changes to the backyard. The previous owners had an area in the middle of the yard that was full of plants and bushes:

The house is a split level, so one side sits on a crawl space. The two gutters on that side go underground and drain into the middle of this patch:

During the spring and summer, the area between this patch of plants/bushes and the fence becomes a swamp after a rain. It takes forever to dry, leaving me to either not mow that area or tear it up with the mower's tires.

My question is, do the gutters have to drain into this area? Or can they drain at the base of the downspout like the other 3 on my house? I'm afraid if I ask landscapers this questions during an estimate for removing the area, they'll tell me it can be changed because they want work and money.

Thank you for any help.