Additionally, as you do not come from the same country or culture as your host, he or she or they will surely be aware of this, and will be very forgiving if you unintentionally do or say something which would otherwise offend them.
otherwise 是副词,在本句中,指如果没有这样做,就不会冒犯他们的意思。可参考《韦氏高阶词典》的释义2: if something did not happen, was not true, etc.
在翻译本句时,汉语里可以不翻译这个词。后半句的大致意思是: 如果你无意中做了冒犯他们的事或说了冒犯他们的话,他们会原谅你的。
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