Background Verification

Hi Guys, I am currently working at a startup and was previously working at an IT MNC for 3 months. I was put on the bench and laptops/assets were not even delivered for 2 months of requesting. When the assets arrived there was 3 weeks of compliance and regulatory training before which my position was eliminated as a result of business restructuring and downsizing. I got my startup offer (strategy type role)by then and I resigned from the IT firm with proper reliving letter and fnf settlement. I have now got an offer from a boutique consulting firm(after working in my startup for around 6 months) . I have however not mentioned this IT mnc in my resume at all since I did not gain any kind of work experience at this firm and it was not adding any value to my resume in terms of the types of roles I am looking for, I wanted to keep my other internships and startup tenure as they were more valuable. Is this going to cause an issue if I undergo a bgv process in my new firm? I have all the proper exit documents and there is no overlap of employment anywhere. Please advise. I am a 2022 pass out.