Hi Kirsten,
Check out these resources:
https://extension.unr.edu/publication.aspx?PubID=2364#:~:text=The%20cheatgrass%20control%20methods%20available,%2D%20to%20two%2Dyear%20period.

https://solvepestproblems.oregonstate.edu/weeds/cheatgrass

There's not much to be done at this time of year since the plants have already set seed. You can mow the plants to reduce risk to pets and livestock, but another crop of cheatgrass will germinate this fall/early winter. Using herbicide in the fall, winter, or spring  is a good option. After you've reduced the cheatgrass seedbank, you might consider planting some desirable vegetable. If there's no irrigation on the site, a fine fescue or a wheatgrass might be a good option.

Thanks
Gordon