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Just what I wanted to know too

If you control your private key, you can claim gas.
And they aren't gonna make a wallet where you don't own your private keys.
I can't tall you if you can claim gas with this app, but if you have your private keys, you'll not lose gas.

qed hit the nail on the head. I'll write a blog post more about the NEO gas system later as I think there are some misunderstandings as to how it works, but we will support claiming gas directly from your O3 wallet