Delivers suspect walk-on part? I'd stumble over scenery (10)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

I’m not quite sure how this fits together: EXTRA (walk-on part) + a reversal (stumble over) of SET (scenery) I’D – or is it an anagram (stumble) of I’D + a reversal (over) of SET (scenery)?