Sharon Wood said she heard that Harriet Green was in line for a lucrative bonus-related payout only through the Sunday newspapers, and that she hopes to donate a third of it to charity on Wednesday.
Ms Wood told a London press conference: “If Harriet Green feels the need to offload some of that money to salve her conscience, that is her decision to make, but to try and gain public empathy by attaching her donation to the memory of my Christi and Bobby I find abhorrent.”
To suggest that her family have anything to do with it is “simply wrong and I wish to make that clear now”.
It has been reported that Ms Green could receive 6m shares next month, and she said she will give 2m of them to a charity to be chosen by the children’s parents.
She led Thomas Cook until last year, during a period in which the firm took legal action against the hotel involved and fought to stop inquests into the children’s deaths taking place in the UK.
Thomas Cook has been hit by a new wave of public criticism after an inquest jury decided this month that Christi, aged seven, and Bobby, six, were unlawfully killed and that the holiday giant breached its duty of care.
The children were found dead in a bungalow in the grounds of a hotel in Corfu in 2006.
They had been on a Thomas Cook holiday with their father Neil Shepherd and his partner — now wife — Ruth, when they breathed in fumes from a faulty boiler.
An angry Ms Wood suggested that Thomas Cook should “reconsider” handing out the bonus because the success of a family-friendly company should not just be about money and share prices.
“It must also consider the wellbeing and safety of its customers whilst on holiday and the way they are subsequently treated,” she said.
The size of Ms Green’s bonus is “a matter for her own conscience”, according to Ms Wood.
She added: “We believe that when she took the helm after this tragedy she did not move the company on with sensitivity towards us as a family.
“If the company’s brand has suffered, those at the top of the organisation must accept responsibility in relation to the decisions made over the handling of us as a bereaved family.”
Ms Wood flatly denied that the children’s father had received a letter offering a meeting with Ms Green. In fact he has still not had a response from her despite writing to her on at least five occasions since July 2013, Ms Wood said.
She added: “As for me, Harriet Green has never had the humanity or compassion to write to me as the bereaved mother of Christi and Bobby and, as far as I am aware, she makes no claim to having done this.
“I would have liked to have met with Harriet Green this week but I have been told that she is out of the country.”