Recent graduates can have access to their school email. You can add a new role to the recent graduates and be able to remove the access at a given time.

Here's how:​​​
  1. Create a clone of the Friends role and name it something like "Recent Graduate".
  2. Assign the "new" Alumni to this cloned role. (Can use Data Import>Role Membership for this.)
  3. In integration settings, enable the new cloned role.

Then, once the time has transpired (say, mid-August), edit the integration settings to no longer allow this role for integration.  And, go to Core > Security > Roles > Recent Graduate > Members to remove all users from this role so it can be re-used again next summer.