Glossary
What is Suppression list?
A suppression list, or do not contact list, keeps the minimum details needed to make sure people who opted out of marketing are never sent it again, instead of deleting them.
When someone asks you to stop, the ICO's direct marketing guidance says you "should put their details onto a suppression or 'do not contact' list, instead of deleting them". A deleted number can come straight back in with the next import and be texted again, which is exactly what the person asked you not to do.
Suppression sits comfortably with the right to erasure. Article 21(3) of the UK GDPR says that once a person objects to direct marketing, their data shall no longer be processed for those purposes, and the ICO's view is that keeping a suppression list isn't processing for direct marketing, so people have no automatic right to have their entry deleted. Keep enough to recognise the number and delete everything else you don't need.
In CaptiFi Connect the account's opt-out list does this job. A STOP reply puts the number on it and any later send to that number is refused, whichever contact list it arrives in, so leave the opt-out list alone when you clear out old contacts.