The Text box uses the Rich Content Editor (RCE) which includes the ability to "insert links, images, media, and documents."   I don't think there is any way to block students from using the tools in the RCE.    Perhaps it's a matter of writing very explicit instructions for the assignment that you will only accept typing that is done in the text box (and that they are welcome to copy and paste from their document, but that you don't want an upload or link).