If the T-top is 6", your duct should slip right inside it. If it is larger, you will need a transition piece to adapt your duct. Hopefully, the installed t-top is not smaller than your duct...
And yes, I would remove the screen, especially if it is as fine mesh as window screen, as it will eventually load up with greasy grime...

So do I attach them with caulk/mastic or something else? Or go out on the roof and put a few sheet metal screws through the two pieces (and then cover those with caulk or mastic)?

Thanks!

I say leave that screen in place. The damper at the hood may help keep critters from coming directly into the house, but you really want to keep them out of the vent turbing and the T-top, as well. When you say "t-vent," I'm picturing something that looks like a roof jack for an attic vent with the opening and screening on the underside of the outer arms to the cross-bar on the tee. Around here, wasps & yellow jackets would be the biggest worry -- their nests could plug up your vent. Nasty to try to clean out.

As for attaching the tubing, metal vent tubing comes in sections that plug together -- a slightly crimped end plugs into a slightly expanded end of the next section. The roof connection will be the same -- the top end slides inside the base of the t-vent. (May be a mite tricky getting it all to snap together with the roof unit already in place.) A couple of self-tapping screws through the vertical sides of the tee into the top ring of the tubing would be good if you can do that. The t vent may have screw holes already.

Caulk would be okay -- but probably not ordinary vinyl painter's caulk because your local government code people might require a fire-rated caulk as you would with a chimney for a wood stove. It is readily available, just more expensive and more durable.

Regardless, you also want to wrap and seal each duct joint with duct tape. (That's actually what duct tape is for.) For this application, you really want to use the aluminized tape instead of the "handyman's secret weapon" --- the common vinyl-cloth duct tape. The vinyl-cloth stuff just won't hold up very well in temperature swings you get in the attic and on the roof. If you have hot summers, that attic and underside of the roof will get very hot. Cloth duct tape softens and degrades in high heat. It also loses its grip in very cold weather.

If you live in a place with cold winters, you also probably want to consider adding a second damper up by your t-vent. That mitgates the chilling effect of a cold column of air above your stove vent, particularly on windy days.

This post was edited by JWVideo on Tue, Jan 28, 14 at 12:35