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We used to use Priority Pass at the market our airport has on arrivals, and what we would do was have the PP scanner ready, and have a screenshot of our arrival info, but zoom in a bit, then just read the flight number out loud quickly.
Haven’t had issues.
With Capital One Lounge, we zoomed in far enough because they scan the boarding pass where it doesn’t show the flight info, and normally talk to the agent at the same time.