The South African athlete's probation officer Annette Vergeer revealed at the North Gauteng High Court in Pretoria on Tuesday that Pistorius had sold one of his cars for 375,000 rand and offered the proceeds to Steenkamp's family, but it was rebuffed and described as "blood money".
Ms Vergeer said: "He sold his last asset, his motor vehicle, and requested the amount be paid into the account of the Steenkamps' lawyers should they wish to accept the amount. I was informed they did not want the money offered by the accused."
Cross examining Ms Vergeer, prosecutor Gerrie Nel said: "Did you know that the deceased's mother went so far as to says she does not want blood money?"
Ms Vergeer replied: "You can place it on record now that the money was in fact rejected and no further legal action would be taken."
Monthly payments of 350 rand from Pistorius to the Steenkamps as a form of maintenance have now stopped.
The six-time Paralympic sprint champion claimed that he mistook Steenkamp for an intruder when he shot her through his bathroom door on Valentine's Day 2013 and has indicated remorse for the killing.