Do we need to maintain H1 after getting GC EAD?

No, but it can be a back up if you did not receive your gc before your gc ead expires.

Yes. Just in case your GC gets denied, you would want to remain in status. It is like an insurance for a worst case scenario. But buying an insurance depends upon your personal preference. Last edited: 29-May-18 02:02 PM

It's better to maintain if you can. However, it is not a requirement.

@Feb-march, its not required. In fact you can save the money that you pay for USCIS if you start using EAD. In case, you did not get your GC in time, you can always extend EAD. Worst case scenario: if your GC got rejected (yesto nahos), you can always go back to your H1 status again.