Thanks for writing. You should be able to deter the grape hyacinths by cutting them to the ground with your lawn mower first thing in spring. They need to spend the spring gathering energy --- so if you cut off their leaves right away, they'll start to dwindle away.
You can also look at covering the area with a good thick layer of mulch. That may deter the grape hyacinths from growing.
---Justin, Senior Garden Editor, BHG.com