Is there a sin upon one who ate a chicken hamburger bought from a market in a foreign country, after initially refusing it by saying "I don't want it," then ate it after his Muslim friend told him, "Eat it, it's on me," and he forgot to say "Bismillah" and "Allahu Akbar"?

It appears the questioner is in doubt about the permissibility of the meat they consumed. We address this in two points:

1. Eating the slaughtered animals of the People of the Book when in doubt about their lawful slaughter (dhakāt): Scholars differ on this matter. Some have permitted it, as the default principle is permissibility. Others have prohibited it, as the default principle for slaughtered animals is prohibition unless their permissibility is established.

2. Omitting the Tasmiyah (invocation of Allah's name): The Tasmiyah does not render a carcass permissible. Rather, it is prescribed when the eater is in doubt whether Allah's name was pronounced over the slaughtered animal or not.

Based on this, the questioner's consumption of this food despite their doubt about its permissibility falls under the aforementioned scholarly disagreement. The omission of the Tasmiyah does not affect the ruling as long as the doubt is about the principle of the slaughter itself, not about the Tasmiyah. The questioner is advised to be diligent in what they eat and to consume only what they predominantly believe to be permissible.