also: とこを
although (it is a certain time or condition); even though normally
Used to express that an action occurs despite an unfavorable or unexpected time or situation. Often follows a noun or clause describing the circumstance.
お忙しいところを、わざわざお越しいただきありがとうございます。
Thank you for coming all this way despite being so busy.
雨が降っているところを、彼は出かけて行った。
He went out even though it was raining.
Thank you for taking the time despite how busy you are.
I was saved just as I was about to drown.
Just when I'd finally managed to get the day off, a work call came in.
にもかかわらず is a formal, written-style 'despite', whereas ところを is more conversational and often used in polite apologies or expressions of gratitude tied to a concrete situation.
Derived from the noun ところ (place, time, situation) combined with the particle を, grammaticalized into a conjunction/particle meaning 'although at that time/situation'.