Gore Keto, your dhoti company does not need to know about your H1b transfer. Just intiate the process with Tech Mahindra and once h1b is transferred you can simply quit your dhoti company. 

I hope you haven't signed any bond or anything with your current employer, even if that is the case its illegal of them to do so. Just go about it normally like people normally do and there shouldn't be a problem.

And yes, you do need to transfer your h1b to tech Mahindra in order for them to file your GC.