can you be a bit more specific about which export function you're talking? My guess is that you talk about the search results in the list view of many Jira issues as described in the docs here.
If that's the case, I don't think there's a way to restrict it. My main question would be: Why do you want to restrict it?
If the people have access to the data, they could export the data in other ways like:
If you elaborate on the reasons, people here might be able to help you further.
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