No thanks to his gallantry for that.

他向你献殷勤你又何必感激。

youdao

I have no idea whether this poor woman kept the roof over her head; all I know is, if she did, it would have been no thanks to Mr Obama.

我不知道这位贫穷的女人如今是否能保住自己头上的屋顶，但我知道，就算能够的话，她也不会再感激奥巴马先生。

youdao

No dessert for me, thanks. It was as much as I could do to finish the main course.

谢谢，别给我甜食了。我吃完这道主菜就不错了。

《牛津词典》

No problem. Got to go.I'm double-parked. O.K. Thanks.

VOA: standard.other

While the city's economy booms (no thanks to him), most people will clap and cheer.

ECONOMIST: Ken's record

Unremarkable IPO aside, Facebook is a runaway success, no thanks to any amount of faux democracy.

FORBES: News Flash: You Never Really Had A Vote On Facebook Anyway

If it has, it is no thanks to what governments (least of all Japan's) have done so far.

ECONOMIST: Transparent hype