A perfect example of the failure of the gravel-over-plastic plan.
What is to the left? A wall or patio area? What is it you are wanting to grow there? How deep is that gravel? If there is plastic under, hopefully that will at least make gravel removal easier. The gravel is so pretty, hopefully you can find a more appropriate use for it.
If you want a cultivated area separate from that vine-ish grass, the barrier needs to be more solid. I have this grass and a bunch of others & they exploit any barrier weaknesses.
That doesn't look like one of the grasses that will get under the type of barrier in the pic, but will absolutely find those cracks. I would put the barrier bricks as close together as possible and use your shovel to cut all along the outside (grass side) of this border to sever all ties between the grass on the grass side and the grass on the rock side. Then the grass on the rock side can be completely removed.
If you haven't done so in the past, you may want to call "call before you dig" because there's some kind of plumbing in this area. That white circular thing connects to - something underground. If you call, they will come to your house and spray-paint where your buried utilities are. Take pics of the marks for future reference. If you damage your utilities digging around, it could be expensive to fix. But if you call first, if you cut something digging in another area that wasn't marked, you aren't responsible for the repair.
If that was my area, I would work on rehabbing the soil this year, adding plants next year. Soil that has been under plastic for any length of time isn't going to instantly grow great plants. It needs some compost/easily decomposable organic matter, and time for the microbiological processes to return some fertility and healthy structure to the soil. For now, you could use pots.
