You could scalp it down with a weedeater and then put your fabric down
Bryant has it down....
The fabric will kill anything you lay it on top of. The issue is wind getting under it and "removing" it. Small squares in your yard are no problem. But longer runs the danger goes up.
Remember these picture anyone?
That was a bad day to be in the nursery business! We had put down 15' wide X-cell fabric covering about 125 x 200 (if memory serves).
The next weekend we fixed it:
And added some BIG rocks:
It hasn't moved since :)
-John