In a statement on behalf of the slain model's parents, lawyers said they had "honoured" a request from the athlete not to reveal payments of USD 540 made each month after Pistorius killed her on Valentine's Day 2013.
"We were therefore quite surprised yesterday when this fact was disclosed in court without any prior warning to us," the statement said.
During a sentencing hearing yesterday, a defence witness referred to the payments as evidence that Pistorius was remorseful about shooting his 29-year-old girlfriend four times through a bathroom door, believing she was an intruder.
The Paralympian star athlete was found guilty last month of unlawfully killing Steenkamp but acquitted of the more serious charge of murder.
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Judge Thokozile Masipa could rule on his punishment as early as Friday, with her options ranging from a fine to 15 years in prison.
Claims about Pistorius's vulnerability and remorse could be central in deciding which way the scales of justice tip.
The defence has suggested Pistorius clean a museum for 16 hours a week as punishment for killing Steenkamp, drawing a furious reaction from the state.
Yesterday, a visibly irate Nel told the court that the Olympian also offered the dead model's family a one off "blood money" payment of nearly USD 35,000, which the family rejected.
"Did the legal team of the accused tell you that the deceased family rejected the offer of 375,000 (rand)?" Nel asked witness, probation officer Annette Vergeer.
Stenekamp's parents have said they will repay the roughly USD 10,000 received from Pistorius "as soon as arrangements can be made in that regard".
"It was always the intention of the parents that the amounts... Would be set-off against any civil claim that they were going to institute," the statement said.
The sentencing hearing continued today with Vergeer being cross-examined by the prosecution.
She had warned that a jail stretch would "break" Pistorius and claimed it was not in the interest of justice.