Defamation is a civil wrong under both Indian Penal Code and the law of torts. To prove defamation, you must establish that SBI's actions were intentional and that they published false information about you, which harmed your reputation. In your case, it might be possible, given the impact on your CIBIL score, affecting your home loan interest rate. The apology letter acknowledging their mistake might act as evidence against them.
However, initiating a defamation case can be time-consuming and also involves certain legal complexities. Therefore, before proceeding, evaluate the costs, time, and potential outcomes of a defamation case. You may consider referring to Section 499 of IPC and relevant precedents like "Ram Jethmalani v. Subramanian Swamy" for a better understanding of the elements required to prove defamation.
On the other hand, as suggested by the expert above, you can also file a suit for recovering damages as well as compensation for mental agony, as proving defamation in your case might be a bit challenging, as there are no strong evidences and prima facie, the case doesn't seems like that of defamation.