Of the stations in Zone G:
There are no TfL buses in Grays itself;
Chafford Hundred (or rather: not Chafford Hundred itself, but Lakeside shopping centre) has two TfL Routes - 370 and 372 (plus the First London commercial route 265, which I think doesn't take travelcards/oyster cards). (Ensignbus are the sole operator in Chafford Hundred itself, although the 370 did used to go here, as indeed it used to go to Grays and to Tilbury)
Ockendon has the 370 and (somewhat infrequent) 347.
(There is one Essex County Council tendered route, the 269 from Brentwood to Grays, operated by Imperial, that passes by, and through the edge of Greater London, around North Ockendon, too: I don't think that Travelcards are valid, despite it being, for a bit, within Greater London)
Purfleet: no TfL buses.
In fact Arriva now only operate one route in Grays (as opposed to from their Grays garage) - the 5 all the way through to Basildon and Southend. Apart from a few Thurrock and/or Essex County Council tendered services operated by the likes of Imperial, Clintona, and I daresay other small operators that escape my mind.
Ensignbus are the main operators there, and indeed across Thurrock as a whole now - with a small network of mostly commercial routes, a few brand new buses, and generally maintaining the high reputation that they have gained for themselves on each of the occasions on which they have operated passenger bus services.
I presume it was c2c's enthuisasm to establish a ticketing element of an "extended metro" service that led to zone G being invented: traditionally (unlike Potters Bar) the buses there were London Country (and their various successors), not red London buses. (Indeed the 370 was only formally brought into the TfL network quite recently, and the 372 is a newish route). That....and some of the cheaper fares they used to offer (e.g. weekend special returns) were abolished within zone G once Oyster availability was extended there...
It's a slightly different situation from places like Waltham Cross/Abbey that are (only) just outside of Greater London (so the station is outside the zones), but, also a natural or well-established bus terminus for buses into Greater London. But there are numerous inconsistencies around the edge of Greater London as to how these are treated. It surely would make sense to bring that into the zones.