Geese Howard isn't dead in the Fatal Fury timeline
The canon may state he's dead, but now let's look at it. When you use Geese or Billy in Real Bout
, Geese would be replaced by 'Shadow Geese'. He loses composure when the real things arrive (it was pretty normal), but if he's not, he is as composed as Geese, near-perfect imitation. Thus, Terry would've killed the Shadow Geese instead of the real Geese, whereas the real Geese is recuperating his wounds back in the first game, enabling him to appear in the King of Fighters
timeline. And perhaps he would've been the one behind Shadow Geese, telling him to steal the Scroll of Immortality for him, though the shadow decided to use it for his own and Geese either had to take things to his own hands or have the Bogards finish the Shadow off for him.
In other words, Terry's guilt is planned big time by Geese while he safely hid in shadows (and enables him to put Gato in KOF 2003).