In short, Admin cannot delete anything from TINYpulse. If there is a Suggestion, Cheers, or comment that is inappropriate or offensive in any way, Admins can hide it from the Employee Portal immediately from their Admin View by clicking on the lock icon if Suggestion streaming is turned on.
However, be sure to follow up with the person who posted it individually and explain your reason behind the action. Note that Responses are only visible to Admins. go to the All Surveys page in the Share tab in your Admin View to hide Responses from the Shareback report before you sharing with employees.