Hello Donna,

Almost all loans give the lender the right of inspection upon reasonable notice to the borrower and under certain circumstances. 

The reverse mortgage is no different.  Your legal documents (the deed of trust) contain the following verbiage:

Inspection: Lender or its agent may enter on, inspect or make appraisals of the Property in a reasonable manner and at reasonable times provided that Lender shall give the Borrower notice prior to any inspection or appraisal specifying a purpose for the inspection or appraisal which must be related to Lender's interest in the Property. If the Property is vacant or abandoned or the loan is in default, Lender may take reasonable action to protect and preserve such vacant or abandoned Property without notice to the Borrower.

The lender has no more right or authority than you give them when you sign your legal documents.  If you look at the content, the lender may enter onto the property only after reasonable notice and at a reasonable time. 

Also, the lender must notify you of the reason for the inspection.  If you are not sure why they are requesting the inspection, you do have the right to ask why and to require them to visit at a time that is convenient to you (provided it is not a delaying stall tactic to prevent a valid inspection).