Grandma bird update

Basically, we keep it, we found out is a she bird and a Australian parakeet, we name her "blanquita" but my grandma calls it "pajarilla Barranquilla"(idk what that means) also she's now in a cage with a few things to keep her entertained.

It's been about a month and she hasn't trust enough to let us pet her, idk why, any advice will be appreciated

Oh other thing she's now fat(that's what the bet told us) and we reduce her food but she doesn't seem to be okey with the idea..