Little Savannah Snodgrass -- a 7-month-old Texas girl who was stricken with a life-threatening brain tumor -- remains hospitalized at Texas Children's Hospital in Houston, where her family says she is improving following her operation on Friday.

The six-hour surgery came after her health insurance company reversed a decision that had denied her surgery at her family's preferred hospital.

On Friday, doctors removed the closely-monitored tumor, which had grown in size since it was discovered in March on the left temporal lobe of her brain. A team of specialists overseeing post-operative care for Savannah were able to stabilize her Monday following a seizure due to swelling and bruising on the brain, her family said. She was moved out of the hospital's intensive care unit Tuesday morning.

The baby's mother, Tessa Snodgrass, said doctors are confident they removed the entire growth. The family is waiting on further testing to determine whether the tumor was malignant.

"She is definitely in great hands," Snodgrass, of Georgetown, Texas, told FoxNews.com Tuesday morning. "We are so grateful for that ... I can't imagine going through this anywhere else."

Following a FoxNews.com report, the insurance company Superior HealthPlan reversed its decision not to pay the acclaimed Texas Children's Hospital for the emergency surgery, claiming the doctors there were out-of-network. Savannah's parents fought back, saying the same doctors had been treating the little girl for months, monitoring the tumor and preparing to remove it.

Superior HealthPlan said Friday it will cover Savannah's surgery at Texas Children's "for continuity reasons."

"Our No. 1 priority has been to deliver the best health outcome for this child, as it is for all of our members," the company said in a statement to FoxNews.com. "Superior is happy to have identified a solution that ensures that this child receives continued care from the provider established prior to their enrollment with Superior. We will continue to assist this family in making sure they receive the care they need.

"While we have complete confidence that our in-network providers have the expertise and resources to give all of our members the individual care they need, we approach every member’s care individually. The importance of maintaining continuity of care combined with the complex and timely concerns of the family were critical to this decision," the statement said.