In an unusually fiery meeting this week councillors went against a recommended name, and instead voted on a name influenced by "public appeals".
Grant said the Taradale RSA did not want to be involved in the next phase of the project because he understood it would not be reported back to the steering group, that the design elements would be decided by council.
"Not being a member on the steering group any longer would give me more freedom to express our views on wider aspects on the War Memorial, rather than being committed to the steering group decisions."
Napier RSA president John Purcell said his RSA also did not want to be involved in the design and build of the new memorial.
"If we stayed in then we may have had to agree to the group, by stepping back we can have our own say," Purcell said.
"I may well have [agreed with the group], but I didn't want to be restricted by having a consensus pushed on me. I wanted to actually speak to what the members want here."
Napier Mayor Bill Dalton said choice to be, or not be part of the group.
"We saw yesterday how democracy works, and democracy is not necessarily particularly efficient. I have no thoughts on whether the presidents should or shouldn't leave, or what that does, it's simply a choice they've decided to make."