I raised a similar query recently with the Totara Helpdesk, and there doesn't appear to be a way to restrict this. The only options available to do this would be:
Set up a scheduled report to send them on a regular basis so they just receive the filter results attached to the email. This is the approach we currently use with our Mandatory Training Subject Experts and have done so for a number of years.
Put the report on a dashboard and using CSS code remove the option View Full Report from the report table block so they can only see what is visible on the dashboard.
I agree though, an ability to 'lockdown' the search criteria on a report would be a great addition.
Kind regards
Sue