The terms of reference for the working group set up to implement the introduction of charter, or partnership schools, says the first schools would serve "areas of significant disadvantage" where the risk of educational underachievement is the greatest.
But Ms Delahunty said "that rhetoric around disadvantaged children falls apart when you look at the basic rules that the question has exposed".
"Where you've got a disadvantaged area and some families there didn't get in to a charter school on the first intake, there's no commitment that local children will have priority for the remaining places.
"The Government should just come out and admit and say we want to use public money to create schools where students can be cherrypicked at the expense of local communities."
Under current Government policy, charter schools will be required to accept all students who apply for entrance - until they reach capacity - regardless of background or academic ability.
But they could set geographical boundaries or requirements relating to the specialisation of the school, as long as these were not designed to deny opportunities to students.
A spokeswoman for Mr Banks said it appeared Ms Delahunty appeared worried that the schools would be too popular and would therefore be oversubscribed.
However, she indicated it was unlikely the schools would be able to "cherry pick'' students from other schools.
"It is very unlikely that any student who is doing well in their current school would choose to leave.''
The schools were expected to offer "education that is tailored to the needs of those that are disadvantaged in the current system and will therefore be most attractive to students who are not currently doing well''.