To be clear, are you talking about institutions as the article defines them?

Institutions are organisations or patterns of behaviour built by societies to help solve social or economic problems which the law or private markets cannot fully address.

If I'm on the right track, an example of institutional legitimacy might be, "Banks can be trusted to hold your money" (vs stuffing it under your mattress), and FDIC insurance might be an example of an action to support or create that legitimacy.

Banks, at least as depositories for money, seem worth having...