Basic Notes:
You can throw him out of the startup of all Lariats and GHands but not SPD’s afaik - This makes throwing very risky. Naturally this may be considered as good to know but relatively useless because you really don’t even want to be in throw range anyways, though I find there are times where it’s me needing to claw back a lead, not him, so it’s worth noting. It’s also hilarious vs Lariat spammers who consider it the go-to wakeup / desperation move (Yes, some Gief’s are that bad) and we’ve all thrown Gief out of a GH from time to time.
If you’re going to use any Dashes of any description, use them so that you hit with the tip of the glove, no more. Going further is risking SPD punish. When using said moves, use LIGHT version, nothing stronger. Sometimes you have to keep the chip damage rolling but do not get predictable or you’ll eat a focus, NJ Headbutt or have it stuffed by normals.
It’s not a bad idea to pepper in Torpedo or DLB as they both have enough pushback to keep you out of SPD range if not meaty or deep - Some Gief’s WILL pepper the footsie game with focus just waiting for a bad bad dash punch. Either that or a NJump Headbutt which, as we all know, is one of if not the most ‘stun’ inducing normals in the game so if you’re going to DPunch, do it selectively. Just because the match is going on and not much is happening, that is no excuse to think, yeah, I’ll just lob out some pointless dashes.
Walking up to a TKD Gief then jumping back on wakeup can be used as a wakeup lariat punish (Jumping Fierce) but do not use it often, especially not with meter as you can be hit by EX GH while in the air and that leaves you with him having full control of your wakeup - If not, he’s in SPD range anyway. Do not jumpin on Gief, ever. Occasionally on wakeup can work as there’s a certain point where JFierce can stuff/prevent Lariat for a counter-hit but if you mess this up you will eat a Lariat - Overall it’s not recommended at all. Ultimately do not take the fight to the air, staying grounded is greatly preferred.
There is a certain range where you can blow up his meter-building lariats with a naked lgt.DUpper (Spacing dependant). Alternatively you can also blow up most lariats with an EX Upper but if you’re going to do this be damn sure you keep the followup combo airtight. Failing that, CRoundhouse or DFierce can also work after the first spin.
If you can outfootsie Gief into a point where most/all jumps are punished and his ground moves won’t work, keep him there. A Cornered Gief should be made feel like there is absolutely no alternative other than to walk at you, anything else should be ignored or punished.
Good giefs will have a Sweep or GH waiting for you during his mixups on your wakeup if you backdash (Option Select). Sadly, there’s not a lot Balrog can do to safely get away. Backdashes, jumps and wakeup moves like EX Headbutt are all risky but such is the guessing game. Your goal in the match is to NOT LET HIM HAVE YOU IN SAID GUESSING GAME. Each mistake costs you in arounds 1/5th or more of your whole lifebar.
If Gief is on absolutely no health he has no answer for an EX Headbutt other than EX GH and that, afaik recovers in arounds the same time as your HB allowing for a potential escape but overall I’ve mostly seen EX-HB win. In short, for those matches where you score a UTK or Knockdown and he has barely any health left enough for chip KO, you can EX HB for free if he has no meter, if he does and he just HAPPENS to use EX GH, that is the only option that you may lose to. Ulti, Lariat, GH, SPD, blocking, jumping or throwing will result in a hit and KO.
This likely does not work if they have U2, but I rarely ever see a Gief with U2 for the Rog matchup.