Hello Robert, welcome to Permies!
To get a better idea of what fix would work the best, we'll need a bit more information:
How big is the area? - either square feet of coverage, or how many gallons of water it holds at it's highest.
What is your climate? will the plants you want to grow need every drop of water they can get, or would that volume of water drown them in an average rainfall?
What is your soil/subsoil like - mostly clay?
Any chance the greenhouse could be uphill from this, and just have the beds down in the bottom? (in general, it's MUCH more difficult/expensive to dry out a footing/foundation than it is to dry out planting soil.)
Hopefully some other, more knowledgeable friends here can give you more firm guidance with the additional info; in my climate, I'd be happy to have an "excess water" problem!