Social Security Survivor Benefits Eligibility?

No one should be receiving 2 checks in their name. Your grandfather probably receives his own check and your grandmother (before her death) received a check/payment in her name.

What name is own the 2nd check? Most likely it has your grandmothers name and no one should be cashing a check (bank deposit even) that is intended for someone else. Someone may claim ignorance of the law/fact but that will not keep SS from getting their money back.
Please take your grandfather and go to your Social Security office and make inquiries because, at some point, this money will have to be paid back to SS.
Most likely the problem is the death notice was not received before the date checks/payments are scheduled to be distributed. SS checks/payments are paid for the month in which received (paid ahead) and SS will sometimes even send a notice to return the money for the month a person is reported deceased. They do not enforce this but they definitely will enforce repayment of her benefit as soon as all the death notices reach all departments.
Unless we are misunderstanding something, your grandfather may receive an increase (and it could be this amount) but you need to go to SS to be sure everything is correct. SS will not give you information unless your grandfather is present or he has given you a full authority POA.