Conversations involving multiple participants, allowing collaboration and information sharing in Teams
You're asking to hide a colleague's Out of Office banner in your group chat permanently—not to turn off that colleague's automatic replies. I couldn't find a documented Teams setting that remembers dismissing this banner when you return to the chat. Closing it appears to dismiss it only for the current view.
Turning off the colleague's Out of Office setting would affect their intended availability messaging, so it isn't an appropriate fix. This is a feature request: in Teams, select Settings and more > Feedback > Suggest a feature, and ask for a per-chat option to remember the dismissal for the current Out of Office period.
Microsoft's feedback instructions: https://support.microsoft.com/en-gb/teams/apps-service/give-feedback-in-microsoft-teams