Moonlighting in TCS

I have joined TCS as a BA of a third party company before getting relieved from my previous company.Its been 2 years and now my project is going to convert me into direct payroll.But in my relieving letter from previous company the last working date is mentioned as March 26 and joining date in TCS in Feb 1..So what can I do in submitting the documents?.If I alter the experience letter ,then will it fail in the background check?Can the TCS BGC team fetch the last working day with my previous company?Or If I submit the original relieving letter then my experience of two companies will overlap.Please suggest what I can do..Thanks in advance