What if no relieving letter is given after probation exit?

Sir, I used to work in a small company for five months. My probation period was six months, but I was not comfortable with the job role, so I sent them a resignation letter and also informed the senior manager in advance. I did not receive any response or resignation acceptance from them. After resigning, I pursued my MBA. It's been two years, and I haven't received any communication from them. Now, I have been placed in a big MNC. I recently contacted the HR department of the small company to request a relieving letter. They said since I left during the probation period, they need to speak with higher management. They also never issued any salary slips while I was working there. I got that job through campus placement while I was still pursuing my engineering degree. What should I do now if the MNC conducts a background check?