"Even though you're quite an intriguing person with a few secrets, I still wonder how you managed to attract their attention. As far as I know, those guys have been obsessed with only one thing throughout their existence."
Avilia knew just why the Temple of Time used to create chaos in the past. They were searching for something to the point of being obsessed. It was only because they failed to find what they were looking for despite the amount of effort they put in that they stopped.
Even she didn't know just why those people would take an interest in Gabriel. From what she could guess, the Temple of Time most probably thought that Gabriel had something to do with what they were looking for. Only that made sense for her.