That included players wearing special WaiKids jerseys in a match against the Crusaders, she said.
The contract was for the Chiefs to be the face of WaiKids, a brand that integrates all children and youth health services provided by the Waikato DHB.
Gill said of her signing the contract without having delegated authority, that "it was a misunderstanding at the time".
She "wasn't the only one involved with... either the negotiations... or the contract", she said.
She had never signed a contract on behalf of Waikato hospital before, Gill said.
She questioned why the matter was being brought up now.
It "will not detract in any way, shape or form" from her "governance role as an elected board member", she said.
Aydon said Waikato DHB "has had a long association with the Chiefs since they became a franchise and we have done a number of activities with them over the years to promote public health messages, raise money for our WaiKids children's service and help with recruitment campaigns".
"We really value our relationship with them and believe we have benefited from this over the years.
"They have a particularly strong and proud link with WaiKids. The players have regularly arranged visits to see our kids on the wards and clinics. These visits to the hospital bring a lot of joy and a real boost, not only for the kids but also their families, the staff and the players."