In my experience? Stop using the card.

I think the logic of the promotions is that if they get the card in your wallet/online accounts, you'll get used to using it. If that's the case, then not using the card (and keep using your other, ideally non barclays, cards.) They'll see the spend if they ever do a soft pull on your credit, and they'll know their card has fallen out of favor.

Of course, if you never use the card, they are liable to decide you aren't worth the bonuses. Not obvious what the balance is.