How can one clear their conscience of money taken secretly in childhood from one's grandfather, given that the exact amount is unknown and there is no way to return it without his knowledge, and do remorse, giving charity on behalf of the wronged, and seeking forgiveness for backbiting atone for these sins, and is charity accepted from one's personal money when leaving work before the end of official hours?

What you did is theft, and it is one of the major sins. Therefore, you must repent to Allah, estimate the stolen amount, and then deliver it to the person from whom it was stolen, even if indirectly. Giving it away as charity is not sufficient if you are able to return it to its owner. Regret and remorse for sins are pillars of repentance, but the other pillars must also be fulfilled for repentance to be valid.