Lowercase when referring to the command, uppercase when referring to it as a project or a piece of software as a whole. "grep" is a command with certain behavior; Grep (or GREP) is a tool on Linux.

How does that sound?

There's some reasonable overlap where you might mean one or the other, but to maintain that there's no reason to make it uppercase?

Exhibit A: https://www.gnu.org/software/grep/

Proper nouns should never start with a lowercase letter