Yes you can, using iTunes (make sure it is the latest 12.5 or newer version) click Library > Songs. Make sure you have the cloud icon column revealed and click View and make sure All Music is checked.
You should see all the music available to you for download to your local machine. Click the cloud icon to sort, select all the cloud songs, and delete. This essentially hides them from your view, until you go into Store > Purchased to view your history of songs you've bought in the past.
When you go into Music on your iPhone it should remove all those pesky cloud icon songs
I found this article, which helped me: https://www.igeeksblog.com/delete-hide-purchased-music-on-iphone-ipad/