Please help me in this weird and tricky situation

Hi everyone, I need some guidance on my TCS exit process and its impact on future employment.

I resigned from TCS after working for one month but didn’t serve the notice period. After my resignation, TCS credited two extra months' salary, and later, HR informed me that I had to return the excess salary and serve a negative remark exit. However, after months of no updates, HR recently told me that my resignation was never processed and asked me to resign again. Now, they are offering a "professional exit" with no negative remarks if I repay the ₹40,087 recovery amount (which includes the extra salary and notice period dues).

I have received confirmation that I will get both a Relieving Letter and a Service Letter showing 7 months of experience (April 26 – exit date). However, my Service Letter will have a remark for absenteeism due to being on LWP (Leave Without Pay) from July 29 onward. HR assured me that this remark won’t impact background verification, but I’m still concerned.

Additionally, TCS is refusing to provide salary slips, and I was only paid for 3 months, even though my Service Letter will state 7 months of experience. For future employment, I’ll have to rely on my bank statements for salary proof.

My Concerns: Will the absenteeism remark on my Service Letter cause issues in background verification? Do most companies ask for the Service Letter, or is the Relieving Letter enough? Since I was paid for only 3 months but my Service Letter shows 7 months, will this raise red flags in BGC? Can I rely on bank statements instead of salary slips for verification? Would love to hear from anyone who has faced a similar situation or has insights into how BGC works in such cases. Any advice would be really helpful!