Tamakoma First isn't allowed to participate in the A-Class Rank Battles due to their modified triggers, but we see Kitora and Yoneya, regular A-Class members using (apparently) modified triggers, and they are allowed to be a part of the Rank Wars.
I think that's because Tamakoma used unique/personalized triggers (which Border doesn't approved), whereas Kitora and Yoneya used a modified/customized version of trigger that have been approved by Border.
According to Replica it's because their regulations are too different;Tamakoma First's triggers aren't standardised like Border's normal triggers and are one-off experimental weapons. Kitora and Yoneya's are modified from Border's normal triggers but presumably anyone can modify it that way if they only wanted to.
According to Kako (forgot which chapter, but it was one of the recent ones where she tries to recruit Yuma), A-class agents can customize their Triggers. Still, all the cases of customized Triggers are regular Triggers, like Kitora's pistol being an Asteroid and a Spider at the same time, and Yoneya's Kogetsu which is a spear, while Tamakoma's triggers are made especially for each user.
That makes me wonder if Kitora's pistol has another bullet type, as each Gunner trigger can only use two different types of bullets. I mean, Spider probably doesn't count as a type of bullet, as Lead Bullet doesn't either (Miwa's pistol has both Asteroid and Viper plus LB, doesn't he?), but she never used any other type of bullet. Scratch that, now that I think of it, only few Gunner triggers actually use two different types of bullet, anyway. I can only remember Kizaki's, Karasuma's and Miwa's now that I think of it.
Also, I read on TV Tropes that Yoneya's spear is a combination of Kogetsu and Scorpion, which would make sense since the blade can shapeshift (though it could be Senkuu?), but I never heard anything about that anywhere else. Is there any confirmation of this?
Edit: (Just some stuff I forgot to mention)
I wonder if Reiji's minigun is approved by Border. xD I think he's the only character who have two different Gunner triggers (not counting bullet types, obviously).
This is an old thread, but since it was revived anyway, as Kako explained (forgot which chapter, but it was when she tried recruiting Yuma), A-Rank agents are allowed to modify their triggers, but this refers to Border's regular triggers. As Chippo said, T-1's custom triggers are experimental triggers made specifically for their users, while HQ's triggers are made so that any Border agent can use them.
To vanquish all lingering doubts: more important than the matter of customization, the Triggers T-2 is not allowed to participate in rank wars for have been said to be Optional Triggers, meaning the only ones that are restricted are Full Arms, Connector and Geist. Sougetsu, the minigun etc. should all be allowed, like Timer, Idaten and Makou, which have been made specifically for Kako's Unit, and might spread later on, at least among A-Rank agents.