Background Check - removed service in company to reduce job hopping

I am not sure if i did a mistake while providing information to new company for BGC .
In past I joined a company A (MNC ) and left in 1 month to join a new company B . After 1.5 years I joined A again (rehire) , and coincidentally I got the same user id in company A , that was issued by A 1.5 years ago . Thereafter I worked in company A for 3.5 Years and left it . The services certificate issued by A mentioned start date from the first hiring ( So total duration around 5 years ) .
I am being hired for a new company now. for BGC i provided my employment history as per the Service certificate of A and removed B completely . Since I have done lot of job hopping ( 7 in 11 years) , I thought its good that my history will look some how better and I can show a longer tenure of 5 years in a company .
I am wondering when BGC check is done , will the inquiry yield same result as what is shown in service lettter .
Am i doing right thing by going with service certificate , or I should go against service certificate and say truth myself.

The chance of your exit from A to B and back to A will be uncovered during BGV is high.
"The services certificate issued by A mentioned start date from the first hiring ( So total duration around 5 years ) ."
Do you mean to say A has missed at on your 1.5 years separation in their service certificate?
You are complicating your CV.
Take advice of other members also and do the right thing.