Well, NO, the House and the Senate do not have the power to overturn his ExO, they just wrote their own bill, which had no effect whatsoever on what Perry did with his ExO, which was put the decision about Gardasil in the hands of the parents, and for those that wanted it had to be a mandated vaccine to get Medicaid and insurance companies to cover it, SHOULD THE PARENTS WANT IT.
Is 'rescind' more legally correct instead of 'overturn'?
Whatever you call it, overturn, rescind, here's a chronology regarding Texas HB 1098. You can read about it for yourself, along with some background info, on the HSLDA website:
Wait, so he signed an EO that said parents can get a vaccine for their daughters if they want it??? What was the purpose of the EO if it wasn’t to MANDATE IT?