"You can do the research stuff until you're fully recovered." Tim is good with computers, right? Surely that'll be something to keep her busy until she's healed enough to go running around the rooftops of Gotham again.

"But until then, you're staying home where I can keep an eye on you." he's pretty sure she was expecting a much more serious reaction to everything she'd done than what he'd actually given her, so he feels justified in grounding her for the foreseeable future. Partly for her own health, but there is at least a small amount of punishment in it.