Well yeah, he did say that her spell is faster, and your argument is pretty good honestly. But still, somehow I'm not satisfied. The whole concept of [Delete] is to cut the connection of an opponent's mana from the spirits, so I don't know whether a faster spell could counter [Delete]. She did observe him during that duel with the prince, so I guess she researched it and figured out how the spell works, and seeing it once in chapter 25 proved her theory, but Auger never once used [Delete] on her. Isn't it kinda dangerous for her to act based on little information? Well, I guess she just ran out of time and made a compromise to fight Auger a little too early to please her teacher, and somehow still beat the crap out of Auger.
Edit :
Wait, did Auger ever use [Delete] on Reina? I forgot because it's been a long time. If he did, then my mistake bro. My whole argument is based on little information about [Delete] and the original concept of it, so if Auger ever used [Delete] on her, then forget it.