Can I ignore the "You may be due a refund from your employer" section? My SS tax withheld is only over by .003 cents. I don't want to contact employer for W2-2c.

Yes, you can ignore the message telling you to request a W-2C.  

The amount should not cause any issues, but if it does, round it down on your W-2 entry.

Thanks for this!   I have the same message where it says My Employer owes me $0.01 instead of $0.003 that the original poster mentioned.   I don't need to chase the $0.01 (as it will be more of an effort to reach out to get a corrected W-2), but I'm assuming I can just proceed without any issue as well.  For my specific situation, the W-2 I received was from a company handling my Paid Family Leave.

Yes, you can ignore that message, it is entirely up to you whether to pursue a refund of overpaid Social Security tax.