Will exit drama with ex-company affect MBA admits or placements?

Hey folks, prepping for CAT and aiming for top B-schools. Quick thing — had to quit my last job suddenly 'cause of a family emergency. Didn't serve full notice, and now ex-company wants me to pay a fat amount for notice period recovery. (around 2 lakh)

They’re being super rigid, even though others in the same role left with no hassle. I’m currently unemployed, prepping full-time.

My doubts:

Will this mess impact MBA admits if I don’t get a relieving/experience letter?

Can I just show salary slips/resignation emails as work ex proof?

Post-MBA, will background checks by future companies flag this?

Anyone been through this or have tips? Kinda stressing.

Appreciate any help!

edit: workex = 5 months