All my searches here lead to Canada, which is not perhaps surprising given the source of the question.

First, the only reference I can find to "peintre-mitaine" comes from Quebec, in a collective agreement for the Mines Wabush company. It's right at the end of this document:

"Fusion de la tâche de journalier
- 032- Aide-menuisier
- 177- Opérateur de machines à nettoyer haute pression
- 431 - Peintre-Mitaine"
http://cfcanada.fticonsulting.com/bloomlake/docs/Pice R-SDM-...

So it's a recognised term in the business but apparently a local one.

It seems likely that the sense of it is "peintre à la mitaine". Literally this would mean a painter who wears a painting glove, but I think the sense of "à la mitaine" is less literal. As already suggested by Phil and Lorraine in the discussion above, this expression seems to mean "by hand" in Quebec. The following is from a "Répertoire de créativité lexicale québécoise":

"MITAINE n.f. Vêtement qui couvre la main et où les doigts sont solidaires contre le pouce. —Loc. À la mitaine. À la main, de façon primitive. Additionner des factures à la mitaine. Sans calculatrice. Creuser un trou à la mitaine. À la pelle, sans pépine."
https://delitfrancais.com/wp-content/uploads/2008/02/ledelit...

Here's an example of the expression, from Canada, in a different context, clearly supporting the meaning "by hand". It's about writers using computers:

"Même si j’ai développé un rapport à l’écran, je n’ai pas pour autant cessé d’entretenir un rapport à l’écriture manuelle. Écrire à la mitaine ou au clavier entraîne une virtualité intéressante."
https://www.erudit.org/fr/revues/pa/2011-n20-21-pa0143/10103...

What might this mean in the context of construction work? I think it refers to the type of work they do rather than their employment regime. In any case all construction painters tend to be temporary contract workers. It seems to me that by analogy with writing or doing calculations by hand rather than using a computer or a calculator, a "peintre mitaine" is probably a brush painter rather than a spray painter. On-site spray painting is common in construction, but for some parts you need brush painters who paint by hand.

"Two oil-based-paint tasks were selected. One task was oil-based brush painting of the door frame, pillar, railing, and fire hydrants at an office-building construction site (OP 1), and the other task was oil-based spray painting of the steel structure at a logistics center construction site (OP 2). "
https://www.sciencedirect.com/science/article/pii/S209379111...