In one of my recent project, there was a requirement to disable/remove export button from report viewer (Only for certain set of users).
To achieve this, we had to remove below two permissions from all roles assigned to those users. You can remove one or both the permission to match your need.
- Export to Excel (to remove
download option from report viewer) - Print (to remove
print option from report viewer)

Before removing permissions

After removing permissions

Thanks
References:

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