You probably know this, but Delta's HR has an automated phone number you can use to
- Verify employment
- Verify employment and wages
There's a printout that tells your lender/landlord where to call (or website) and you fill in the numbers that they'll need to use. Pretty sure you have to set up some kind of one time use code for option 2.
Alternately, print the paystub and use a big black market to hide any info you don't want to share.