Most reliable way to cut a straight opening would be by using two straight pieces to bracket the router base with the bit lined up to the cut line. Double stick tape to hold the pieces in place. Use a plunge router and make several passes, each a little deeper.
You could also use a bushing (Center the base first), and make a one time jig that allows for the offset of the bit from the edge of the bushing. Make many passes. I'd use a spiral bit for this, half inch or at least 3/8ths. If the grille has square edges that fit into the opening, trim the rounded corners with a jig saw or small hand saw. I'm assuming this is far enough from the wall that you can have enough room to cut the edge nearest the wall with your router. If it's too narrow, cut as much as you can with the router, then use a jig saw.
As a final resort if it's too tight for even a jig saw to fit, I'd visit a Harbor freight and get one of these. Cheap tool, not used often.
You could also use a bushing (Center the base first), and make a one time jig that allows for the offset of the bit from the edge of the bushing. Make many passes. I'd use a spiral bit for this, half inch or at least 3/8ths. If the grille has square edges that fit into the opening, trim the rounded corners with a jig saw or small hand saw. I'm assuming this is far enough from the wall that you can have enough room to cut the edge nearest the wall with your router. If it's too narrow, cut as much as you can with the router, then use a jig saw.
As a final resort if it's too tight for even a jig saw to fit, I'd visit a Harbor freight and get one of these. Cheap tool, not used often.