No. TD status carries no employment authorization of any kind, and working remotely for a Canadian employer while physically present in the United States is still work performed in the United States. TD permits accompanying the principal and studying; it does not permit employment.
Where the work happens is what matters, not who pays for it
This comes up constantly, because a Canadian payroll feels like a Canadian job. For United States immigration purposes the relevant fact is where the person is physically located when the work is performed. A spouse admitted in TD status who logs in from a house in the United States and does a full day of work for a Quebec employer is working in the United States without authorization, whatever the payroll says. TD is deliberately narrow: it lets a spouse and unmarried children under twenty-one accompany the TN holder and lets them study, and that is the whole of it. It is a genuine difference from other categories, because L-2 and E-2 spouses are employment-authorized incident to status. A household that needs two incomes should evaluate whether the working spouse has a route of their own before the move rather than after it.
Hypothetical example: an architect moves on TN while a partner keeps a Canadian payroll role and a child expects paid campus placement. The household must decide whether each person has authority for their planned activity, using admission records, the actual work arrangement, and the child’s civil record. Record each person’s activity and deadline separately, then sequence admissions, employment, and school steps around those facts. The avoidable problem is that Canadian payroll does not change the physical location where services are performed. Do not proceed until everyone has a plan matching their circumstances.