Echo’ing what Rainscape said.
As a Vanilla player (still) anything I could add would be dated info as I’m unaware of how it’s been effected in SUPER.
Anyhow, just general sidenotes (I’m sure someone can clarify whether what I say is now invalid due to SUPER / AE).
An unsafe but sometimes beneficial trick to know is that on Gief’s wakeup (depending on what the player does vs you being right next to him as he’s waking up) an ‘instant’ jump back roundhouse will hit him overhead and stuff certain things. It’s similar to the usual jumpback on wakeup trick bar the fact you’re relying entirely on him doing something on wakeup to begin with. If he just blocks, you’re in for a punish if they have any form of reaction (Greenhand or Roundhouse will hit you out of the air) but as far as I’m aware it’ll stuff any Lariats, normal Greenhands and mostly any Normal as the Roundhouse will connect right into his face.
Don’t try it too often.
Gief can be thrown out of all reversals bar SPD’s - In short, if you get a terrible Gief who relies on Lariat spam or any form of that low level garbage (Take note if he doesn’t know how to SPD, or doesn’t do it often) have fun throwing him all day when you’re in range. It will beat all wakeup/reversal GH, all wakeup/reversal Lariats though you will pay for it if you mistime it, or if he throws out an SPD (Including Super or Ultra). Naturally Balrog doesn’t aim to get into throw range often as it’s not his optimal distance but I find them to be almost required at times when trying to regain a lead versus a camping Gief holding back, or one jumping over you into a GH thinking you’ll backdash.
Again, don’t try throwing him too often, it’s risk vs reward with often far more risk than it’s worth, situation dependant.
In terms of general footsies, Roundouse is your friend as well as standing jabs. If you’re in optimal distance then there is no low hit he can hit you with other than sweep. Standing Jab into your OWN sweep is exceptional here though some Giefs motion SPD’s for dropped links and it will catch you if you mess up at certain ranges.
Avoid all deep specials (Especially TAP and I won’t even bother mentioning Overhead) - If you’re going to try hitting Gief with Specials, ensure they are from the tip of Balrog’s glove so pay attention to your spacing. If you for any reason doubt your special, cancel backdash is always an option and one he can’t GH you out of (You generally recover in time to block. Alternatively if he throws out an SPD attempt you’ll be able to walk forward into a Normal Punish at best).
Restrict all Specials to LIGHT version outside of Combos at all times. With that in mind:
DashLowBlow and Torpedo often cause enough pushback that Gief can never SPD you on block from them, even when Deep, though he may be able to clip you with GH at certain ranges and considering they’ve more recovery than DS and RU it’s best not to throw them out recklessly. He can and will SPD you on blocking anything other than Light DS (Glove Tip) so restrict your use of Strong & Fierce Dash / Upper to combo’s only.
Gief’s dash is horrendous in both directions so if you see a Gief peppering focus attacks up midrange/close, try above Torpedo when you’re certain he can’t recover into a neutral jump. Again, at certain ranges you’ll be pushed back well out of retaliation range but don’t do it too often.
If you have SUPER or ULTRA, it can be used to punish Lariat’s, failed SPD’s, Focus Attack attempts and also good as an AA at mid range if they attempt to jump in at you due to his slow jump, though in 99.99% of the case you would opt for a regular AA Normal or a Light Headbutt.
Regarding AA, some Gief’s have been smart enough to only jump at a range where CFierce whiffs - This results in a free SPD - Again, watch your spacing, eating an SPD for a failed AA attempt is NOT NICE. If you suspect CFierce is an out of range option, a regular Fierce will do the trick or TRADE at worst but that is better than being SPD’s or having Gief even closer.
Last but not least, on so many occasions I’ve scored a UTK on Gief who ends up with literally a pixel of health. In this scenario, he has ABSOLUTELY NO ANSWER for an EX Headbutt on his wakeup other than EX GH - If this happens you’ll either both end up at neutral frames or have the advantage. If he has no meter, it’ll 100% KO.
Again, as a Vanilla player, I have no idea how the above would result if Gief has Ultra 2 - Can that be activated on the ground and, if so, does it catch EX Headbutts?
All I can think of right now and bare in mind, not only may some of that info be false to begin with but some may not even apply to SUPER anymore so I’m just trying to add extra onto what Rain has said.