You can't cover the grate, and your only alternative is to see if it can be moved. However, this will certainly impact your floor. Are you changing the floor soon?

Thanks for reply. Not replacing flooring any time soon. How about using Flor carpet squares and leaving an open spot at outer edge for grate?

That is what we did in the hallway,,got Flor carpet and adjusted the size for what we have. You could do this for both corners so that it looks like you wanted a different design for the carpet:)

Printesa is correct. Your carpet can have irregular outside edges for a modern look. Don't try this with borders but with a scattered or random pattern it would be fine.