If it comes down to a "fix it or replace it" issue you could take the covers off and throw them in the washer on the gentle cycle. Dry them for a few minutes, then put the covers back on the cushion and speed dry with an air mover.
I've done that a few times over the years with decent success. The one issue I've had though is it can lighten/change the color a bit. In your case, it looks like the color is screened on and not part of weave, so the pattern shouldn't change, just the background.