Can a home care agency make caregivers sign a non-compete in Delaware?

Generally enforceable if reasonable. Delaware has no general non-compete statute. Courts enforce covenants that are reasonable in time and geographic reach, protect a legitimate economic interest, and survive a balancing of the equities. The only statutory carve-out is for physicians, so caregivers are not exempt by statute.

What about a client hiring your caregiver directly?

That is usually handled in the client service agreement, not the caregiver's contract: some agencies charge a placement or conversion fee if a client hires a caregiver directly. Whether that clause is enforceable is a contract question, so have a local employment lawyer review it.

What should you confirm?

The general reasonableness standard comes from a law firm survey of Delaware case law.

General information, not legal advice.