To complete this you need to enable 2 things:

Enbale Parents to Edit Grandparents profile information they are related to
  1. Navigate to Core, select Security, then Profile Access 
  2. Select the Profile Relationship Access tab 
  3. In the Dropdown box Select Parent 
  4. In the left hand column links select Grandparent of Student
  5. Click Edit in the top right and select the fields you want them to be able to edit, view, or not view
No= They will not see these fields 
View= They will see these fields
Edit= They can edit these fields for the relationship being added
When all selections have been made Click Save

Then you will want to add the Relationship in the Parents Profile to list their Parents (Grand Parents)
For example you have Paul Dutton's record pulled up (he is the Parent of Students Sue and Bob). His Parents are Joe Dutton and Francine Dutton you would add the Parent relationship type for Joe and Francine to Paul's Record. Paul's Children are Sue and Bob. When Paul views Sue's Contact card this will list Francine and Joe as Grandparents of Sue (provided the relationship from Student to Grandparent has been added). Paul can click into Joe's or Francines record now and edit the fields selected in the above steps.

You do not need to provide Parental Access or List As Parent for the Grandparents that are Parents of the Parent.