Worried About Background Checks? How My Past IT Job Termination Might Affect Future Offers

I worked in an IT company for two years from May 2007 but was declared absconding and terminated by the company in March 2009. I was unwell and unable to meet their timelines, and my manager didn't cooperate at that time. I contacted the company physically on various occasions to settle my full and final (FNF) later. I also tried in 2015 through emails, but they didn't respond. I restarted my career in a different domain after that. Recently, I resumed my career in IT and have been working there for two years. Now, I have received offer letters from some big companies. Will this impact my background verification (BGV) with future organizations?

It is not likely. Your earlier tenure of 2 years is now nearly 15 years old. Unless you mention it in your resume, it may not surface at this point in time.