I am a Data Scientist @ UBS and have 2+ years of work experience and at present I am pursuing my Master's too, hence I would like to put forward my perspective.
a) In India, I would say your educational background is quite important. Not only degrees but from which college have you obtained them is also a criteria for some companies (it's not correct, but leave that for now). Most Data Science JDs if you see have Masters (minimum) required.
b) At present, I am pursuing my Masters in Data Science and Eng. from BITS Pilani. It's a WILP (work-integrated learning program). Prior to joining BITS, I did my research and found many foreign universities offering a Masters in a similar major. However, their curriculum was at par to say the least, so I dropped those. Another very good option was opting for a Micro Masters from MIT (via edX). On successful completion, you get awarded certain credits which you can then use to pursue full time masters from a premium institute in abroad. But, remember you wont get a Masters degree once you complete Micro Masters. It's just a stepping stone to your Masters from abroad.
Up until now, I haven't encountered a situation where recruiters have explicitly asked about my Masters. However, I know somewhere it gives me an edge while I am applying for DS related positions.