Here are a couple of photos of the ivy bed with the bald patches and the wayward grass.

Are you sure that is grass? How large is this bed?

Need to see a large, overall area of ivy. Include some surroundings.

While it would help to have some extent of the problem, know that there are grass-killing herbicides that are meant for use in groundcover beds. I don't have a lot of experience with them so can't offer a comparison or tout a favorite. Surely, there will be some reviews of them online that you can explore. Search "grass killing herbicides" as a starting point. From the picture, I can't tell if what you have is actual grass, or a grass-like plant. Maybe you could find other examples to photograph.

It's hard to say without being there to explore myself, but the bald spot in the picture looks as if it is primarily dead material that is comprised of other material. Ivy grows fast enough that any small dead spot can heal over pretty quickly from growth of the surrounding material.

In the picture, I see also other broadleaved plant material. The ivy will look its best (less weedy) if all other material is removed.

When needed, I use this product for grass that I cannot pull from ground cover.

Nutgrass is a sedge so it will not work on nutgrass. I think you should try to dig up a section of the "grass" to identify it. It looks like a bulb to me.

I agree that the 'grass' doesn't look like grass. There seem to be two different plants there, both of which strike me as being bulbs/corms.

Thank you so much for your time. I will take a few more photos and upload them. Fyi, the "ropey" areas are very tight and close to the ground.

When watering your ivy, consistently check the dirt before including water. Ivies want to be kept somewhat on the dry side, so let the dirt dry out a few (dry to the touch on top) before you water your ivy plant once more