Is wearing a khimar that attracts attention in a society unaccustomed to it, with the intention of modesty and seeking Allah's pleasure, considered a violation of the condition that the hijab should not be for fame?

A woman is required to cover what Allah has made obligatory to cover. The priority is for the clothing to be customary in the country and not draw attention. If the obligatory covering cannot be achieved except with unusual clothing, then it is incumbent to adhere to it, even if it attracts attention, because acting according to the Sharia takes precedence over custom. The garment of fame (thawb al-shuhra) that is prohibited is what a person wears to distinguish himself from others out of arrogance and pride. This does not apply to someone who wears legal (Shar'i) clothing to please Allah the Almighty.