I think by law, they’re required to mail it by the end of Feb, even if you agree to getting everything else online.
I’m guessing by what you’ve said, you didn’t download or keep any copies of monthly statements? Even the last one from before the re-fi? Most lenders include prior year interest paid on monthly statements for the following year.
You have 4 days. I’d use the number they gave you and get your return filed, though as a practical matter, there is no penalty for filing late unless you owe money. Penalties are based on the amount you owe. (there are some penalties that are rarely assessed based on total tax, irrespective of when it’s paid, so don’t wait too long after 10/15.) If it turns out the number they gave you is significantly different, you can amend, though that’s a PITA.