Been there!
I put down that grey landscaping fabric that kind of looks like felt. I put it all over and then covered it with 8 inches of wood chips about 15 years ago. And I've regretted it for years. I still find that stuff out in my garden and orchard, only now the tree
roots have grown through it and it's impossible to pull up.
You've just got to get out there and pull it up. The problem is that it sort breaks down after a while and when you try to pull it up, it turns into a mass of fibers --- almost like a spider web. The sooner you can pull it up, the easier it is.
What I hate about it is that you can see exactly where the mulch stops and the soil begins: the broken-down mulch is black and beautiful, while the soil beneath is grey, lifeless clay. The worms don't even want to go down to the clay soil, and even if they did, the fabric stops them.
It's one of about 500 things I've done over the years that I deeply regretted later.
Hang in there!
"The rule of no realm is mine. But all worthy things that are in peril as the world now stands, these are my care. And for my part, I shall not wholly fail in my task if anything that passes through this night can still grow fairer or bear fruit and flower again in days to come. For I too am a steward. Did you not know?" Gandolf