Sheile Coleman, from Hillsborough Justice Campaign, expressed sympathy with Anne’s situation.
Mrs Coleman said: “The support has given Anne such a boost. She is uplifted by it.
"She knows it may make no difference, but that said, the petition being debated cannot do any harm.”
Mr Grieve said the application for fresh inquests was not yet ready, partly because he had consulted the families of all the 96 victims, who were given one month to respond.
He told MPs: "I expect to make that application in December. I will do all I can to take this process forward as quickly as possible."
Mr Grieve also stressed the timetable for the High Court to act was out of his hands, saying: "I obviously can't predict the timetable for the fresh inquests to take place."
And he repeated his warning that any criminal proceedings against individual police officers or organisations involved in the alleged cover-up could delay the inquests.