At the outset, it should be made very clear that Limitation Act 1961 applies to every debt in India and Banks are not, repeat not exempt from the aplication of this act. So if you have cleared all your debts and you have not signed any paper to the effect that the debt if any is acknolwedged before completion 3 years of such debt, debt if any shall be barred by limitation. If as a good Customer, you wish to pay, you an very well pay, quoting your Card Number etc. by writing the cheque, as already advised, ICICI Bank account followed by your name (as noted on card) and followed by card number. On the reverse of chque also write card number.
Now the menace of calls. Generally, unless a serious flaw is there in the Bank records, matters shall not be handed over the recovery agents, who follow up for recovery. Therefore, verify your records and find out the card number and with Card Number send a mail to the Customer Service.
Preferably, send such letter to the Bank by Registered Post with Acknowledgement Due, by Indian Post and not by some Courier who normally not give Proff of Delivery (POD). Ensure that resonable time passes and if still you are not getting reply from the Bank and the Agent is still calling your family, file a case before Banking Ombudsman C/O RBI Regional Office under which your residence is coming. For more details on how to make complaint to Ombudsman and the format etc. please visit the website of RBI. You may use the following link to read FAQs
https://rbi.org.in/SCRIPTS/FAQView.aspx?Id=24
The key is tracing your Card number and with it initiate correspondence with Bank and if reply is not received seek relief from Banking Ombudsman.