Just thinking out loud really.
Catherine could invite them, but still ensure the focus is not on them. It's not a live event and is highly edited before broadcast. I assume Catherine has a fairly large degree of control over the final broadcast edit.
Could be done in a way that the Sussexes arrival is filmed, but little time spent on them (just enough to know they are there), seated a row or so back and not in eye line or in camera shot with the Waleses, so only very brief views of them during the Service, then a quick shot of them leaving.
That might be a way to get it over with, but still keep the focus on the Service? You don't see Catherine interacting or greeting every single guest, the Sussexes would be in and seated before the Waleses and other Royals arrive.
It should be Catherine's decision at the end of the day, and should only happen if it's what she wants, she is in no way obligated to extend any branch of reconciliation or friendship to them. Certain segments of the Press and absolutely the SS will crucify her regardless of what she does. So fuckem is what I say