You can easily turn Round-ups on and off. Here's how:
Log into your Starship account
Tap on the double arrows for Money Movement
Tap "Collect spare change"
Round-ups is now paused. Don't worry though, while you have it paused Starship will remember how much you had collected and resume from that point once you re-enable it.
No money will transfer from your linked checking account to Starship until you re-enable this feature.