"I'm an educator myself so I said, there's no way the teacher really did this," Green told KVIA-TV. "I didn't want to believe it."
Green said she contacted Juzdowski, who admitted to creating the drawing because the boy was not paying attention in class.
"She admitted to embarrassing the children rather than punishing them," Green said.
Green said the teacher emailed her an apology reading: "I'm sorry [the student] took offense and I totally understand if you would like to meet with an administrator and have him moved."
Green said El Paso Independent School District officials told her the teacher will not be removed from her position.
"Their reasoning was that she admitted it," Green said. "Had she denied it she would have been removed from the school immediately. But because she admitted it they said it shows she's willing to change."
The mother said she is seeking to have her son transferred to another school.
"If it was a man teacher doing it to a female student, they would have taken this totally serious," Green said. "But because it's the other way around I think they're letting the light side go on it. And I just want him out of the environment."
Gustavo Reveles, a spokesman for the district, issued a statement to website Mashable.
"The teacher has acknowledged that her actions were inappropriate and we are moving forward with adequate disciplinary action. Her actions are not in accordance to our Employee Handbook," he said via email.
