Under RTI act

nationalised banks are covered under the provisions of RTI

but they may deny the information in your case as these are the personal details of parents of your mother.

you will have to prove that your mother is one of the legal heir of her parents thereafter the bank will be able to furnish the details as per the rules set by RBI.

since your a family member under this situation the bank may give the details.  In most of the times the personal details and business transaction cannot be given under RTI act.

If your mother is one of a nominee s  mentioned  mentioned by her parents, in the record of the Bank she will be entertained by the Bank, othewise it is a matter under official secret not to be discolsed to the persons other then account holders unless someone produces the certificate of  legal heir

. Howver, your mother can orally appleal  to the manager in confidence to have a look at the transaction in account , purely as a person favor,  and sypathy to a senior person, in genuine need for such an information.

RTI will not help.