Name the exclusion directly
Say whether you failed to invite them, left them out of a decision, excluded them from information, or allowed a group pattern to continue. Avoid claiming you assumed they would not want to come.
Repair the access, not only the feeling
Share information they should have received, correct the decision process, or make future inclusion explicit. Do not invite them only so they must prove publicly that the apology is accepted.
- Acknowledge whether others were involved.
- Correct practical disadvantages created by exclusion.
- Let them decide whether joining now feels comfortable.
Address the group pattern
If exclusion was repeated or tied to identity, status, conflict, or cliques, one personal apology is not enough. Change the invitation, information, and decision systems around the group.