How do I remove purchased songs from my library?

Assuming that you sync playlists to your iPhone, you should just be able to delete the files from your library. iTunes shouldn't flag up anything when you Check for Purchases since it checks for files you've purchased but not downloaded, not files you've purchased but which aren't in your library.

If you manually manage your iPhone music, you will need to delete the file from both your iTunes Library on your computer and from your iPhone directly.