This is an overview of the most powerful (damage-wise) options each character has post-GI. All listed damage is without tech. Throws are listed for characters who do less than 40 damage or if the throws are powerful. One option listed means slower options do less damage.

Character name
Fast option(s) = free damage/attempt within the 24 frame window if they don't re-GI (damage, notes)
Slow option(s) = free damage if they attempt to re-GI immediately (damage, notes)

Algol
3B QI B 3B (80)
4[K] 3B QI B 3B (91)

Amy
66A+B BT B+K AmS KK (61)
BP B 44K 66B+K AmS K:A (71)

Astaroth
AB (36), command throws
66[K] PT (104)

Cassandra
AS :[B] x4 4BB:A (71)
33B A+B AS :[B] 4BB:A (87)

Cervantes
3B 8A+K iGDR 8B (83)
8A+B:B+K 3B 8A+K iGDR 8B (97-98)

Dampierre
11B 623K:K:K:K:K:K:K:K 4B (128)

Hilde
C3B C3A C2BB C2AA (105, if spun into BT 112)

Ivy
In CL:
CL A+BA+K WP 1B+K CL 4B 236BB (71, requires a step back on smaller characters), CS/SS

In SW:
22B 6B8 (55), CS
SW 44B 66K CL 236BB (64)

In WP:
WP 3[B] SE B:6B:4B:6B:4B (54), SS
1B 2B+K CL 4B 236BB (83)

Kilik
A+B 66B 66B (81)

Kratos
4A 11_77BAA (60)
66B8 SA BB8 IR A:K (83)

Lizardman
3B 66K (67)
11B 6[K] 66B (72)

Maxi
B+K:B:B:BA (75)
9K 33bA RC A 236A (101)

Mitsurugi
A+B[6] 33B (83)

Nightmare
3[B] NSS b:A (74, NTC 87)
66B iWS [B] NSS b:A (85, NTC 100)

Raphael
66[B] Prep K:K 11B (65)

Rock
33B 1B+G 6B+K (62)
214A:A:A 3B+G (105)

Seong Mi-Na
A+B 1K (56)
4A+K 66A+B (66)

Setsuka
agB ag:B JF Umbrella (100)

Siegfried
1B (63)
44A iWS AA (70)

Sophitia
TAS AA TAS B:4 (97)
4[A] TAS B:4 (104)

Taki
11K A:6 WRO B (63)
WRO BKB (76)

Talim
33B:B 2A+B (69)
236[B] 66B 2A+B (75)

Tira
In JS:
4A:A 44K GS 3kA 11K BT 2K BF 66B (116)

In GS:
4A:A BF 44K BF 44K BF 66B (92)
4444B 4B:B:B 22A BF 44K 22B BF 66B (125)

Voldo
6:6B 66B 6:6B 2A+B CR B (65)
[B+K] (75)

In BS:
BCR B 1[K] 2B+K MCHT K (71)

Xianghua
25B 66B+K (66)
4A+B 33KA (71)

Yoshimitsu
3B 4A:A:A:A:A a:B+K 66B (86)
33A+B iMCF 3AB 4A:A:A:A:A a:B+K 66B (103)

Yun-Seong
8K:K:K:K (70)
33(B) CR 8K:K (78)

Zasalamel
44K 66A+B (64)
A+K b:K 6A+BB (96)

Kilik:

Fast Option: i20-Frames
A+B, 66B, 66B = 81
A+B, 46B, 6AAA = 89 (Character Specific; Can't remember but its a respectable amount)
A+B, 3BB, aB = 104 (Character Specific; Can't remember but its a respectable amount)

Slow Option: i27-Frames
4A+BBB = 65

Setsuka:

Fast Option: i23-Frames
ag:B, ag:B, Umbrella JF = 100

Variable Option: i17-Frames
1B:B, 1B:B, 214~3B:B, Umbrella JF, 33B = 92

Cervantes:

Fast Option: i19-Frames
3B, 8A+K, iGDR, 8B = 85+

Variable Option: i15-Frames
iGDR, 22B, 8A+K, iGDR, 8B = 80

*Variable refers to weaker choice but faster in frames so it can be played with either fast or slow.

Ok. Those are all that I've found for now. Credit to SU for the Setsuka one. Inform me if there is a more damaging and consistent option than any listed. Tira has a more damaging one in JS but it only whiffs on Amy. Made me very sad.

Tira:

GS:
Slow: GS 44B, 4B: B , 22_88A , BF 44K, BF 44K, BF 66B ~100
Fast: 4A:A, BF 44K, BF 44K, BF 66B = ~90+
Air: 44K, BF 66B = 54

JS:
Slow: iWS B+KK , 1K ~69
Fast: 4A:A, 44K (moodchange), 4B: B , 22_88A , BF 44K, BF 44K, BF 66B ~126
Air: 44K (moodchange), GS BF 44K, GS 66B ~ 75

EDIT: Oops too late. I added the new "air-gi" thing despite it's not a mixup option, I thought it should be mentioned.

Mikosu:

Dampierre's 11B fits in the GI window. So his strongest fast option would be...

Dampierre's:
11B, 623K JF string, 4B = 144

Also minor correction on Kilik's slow option. It does 70 not 65.

DIdn't know 44K, GS 4BB doesn't work on Amy O.o....

Arnie: Good point about GI-ing TJ moves but it's usually such an anticipatory thing that I'm not sure if listing it is worth it. Wouldn't hurt I suppose. Yea Amy's annoying as ever.

SU: Darn it. Dampy beat Tira in post-GI now thanks to that....besides her whole transition thing :( Circus kicks JF is definitely worth mastering.

Poor Ivy. Small correction:

CL A+B,A+K, WP 1B+K, CL 4B, CL 236BB - 71

SW 44B, 66K, CL 236BB - 64

You can also add the command throws.

I dont even care about BD (not that anyone should) but best combo post GI for mitsu is A+B[6] k:B for 95 (not sure if A+B[6] is the best starter though, but it seems so)
I think MST A+B or 236[B] nets an even more damaging combo (slightly) for a slow option. But I'm not sure if its more damage , its been long ago since I tested.

Those don't work on Amy unfortunately. It's really surprising how her hitbox has gotten smaller.

Don't forget to hate. Everyone loves a hater.

Taki correction: Fast option 66B:A -> 11K A6 WRO B

Tira GS slow amended for dmg.

To add: If NM is in NTC his dmg goes up to 87 and 100 respectively.

What's Tira's best if you're not banking on an unreliable mood change?

JS:
33B 33AA (50)
4KB 22B (63)

GS:
What's already listed.

Sophitia's options upgraded.

Hilde as well: C3B B+K C2BB C2AA (104) to C3B C3A C2BB C2AA (105).

Amy upgraded by 1 point.

Algore slow option found. Yun slow option changed.

i think cervy's best slow option would be FC A+BBBBBBB cause if they reGI they eat 70 dmg and great wake up and if they dont your at +13. Or 66A+B 8A+K iGDR 28B.

mikosu: I checked A+B[6] k:B on amy , it works perfectly

Mikosu are you sure Cervys 8A+B:B+K gives a free 3B on NH in BD??

In SC4 its only +15 like all the JFs, 3B only on ch....that would be a nice buff...