Removing fake experience when joining new organisation - Background verification

I joined a contractor type employment service by keeping 2.10 yrs fake experience. Now I have completed 4 years in current organization and have got an offer letter for permanent position in esteemed organisation. I have shown as 4 years experience only and they have given confirmation to join as per notice period. Now, the background verification is asking for justification for almost 3 years gap in employment. This gap I have corroborated with examinations and preparations (GATE and IES), which i gave dedicatedly, and my failed venture i started.
Now i want to know whether my future org will anything that will highlight the 2.10 years of fake experience ?
Does in background verification find the fake experience ?
Will the present company (contracting company) give details of prior experience?

Hi, the background verification team cannot ask your current hr to share details of your first company as that is irrelevant and your hr is not so idle to take time out to search your first company details and verify them your date of joining/relieving. BGV team can only verify your current employment details. So chill.
I hope you have removed the 2.10 exp details from your resume and linkedin, also do not mention the same when filling up the joining kit. BGV team cannot come to know about it. (Even if somehow they come to know about it, your simple answer should be that I left the org as it was shutting down, they did not provide me any employment proof")
Thanks and Regards,
Akash Sharma