What kind of contract or agreement should the cleaning aunt recruited by the company sign?

In fact, if you don't reach retirement age,

A dispute is a labor contract.

The Supreme People's Court's Interpretation on Several Issues Concerning the Application of Laws in the Trial of Labor Dispute Cases (III)

French interpretation [20 10]No. 12

Article 7 Where an employer brings a lawsuit to a people's court over a labor dispute with an employee who has enjoyed pension insurance benefits or received a pension according to law, the people's court shall handle it according to labor relations.

Article 8 If an enterprise employee leaves his post without pay, retires before reaching the statutory retirement age, is laid off for work, or stops production for a long vacation, and brings a lawsuit to the people's court according to law because of a labor dispute with a new employer, the people's court shall handle it according to labor relations.