It could be Apache Olla basket, or one of a couple of related groups that probably serviced by the schools. The coils are a bit thick which often indicates a later basket. Some of the ones with thinner and tighter coils were earlier pieces made for use, thicker coils often indicate a piece made for trade or the tourist market.
If you can pin down where your grandmother lived that could help you ID the basket. The piece of paper has Phoenix on it, and there was a famous (infamous) Indian Sanatorium there but it mostly served Mojave and other tribes I believe. Not sure if the parents were able to visit the kids since part of the plan was to isolate them from tuberculosis and other diseases. Some of the other that were more school than hospital that were on reservations were better.