As promised I’m posting pictures of our newly improved basement.
What the trench looked like going into the garage: 
What the trench looked like with the drainage system in place: 
The garage wall after the job was completed :
Where I hope to do laundry some day: 
Basically, they cut a trench in our floor and then laid their patented pipe and filled with gravel. Then they applied a plastic film to the wall and then put a rigid plastic sealer over that. After all of that, they put down concrete to make our floor complete. Then, they cleaned everything up so that you can hardly tell they were there. The excellent thing is the concrete has a citrus smell to it so there’s none of “what’s that smell” going on while it cures.