Ask yourself, are they considered invasive where the person lives? Just because they are listed as invasive in one area it does not mean they are invasive everywhere. Take rosemary. Is weedy in the southwest but I can not get it to grow because of different growing conditions.

I am aware of and have considered all that, maifleur.
My question is should such items be brought to attention so that those who don't know that these are invasive weeds will be able to choose?
I believe in education on all levels, including this one.
Such aggressive plants can be charming and beautifying in a large area like a meadow, but can wreak havoc if placed in a flower bed.

There are some people that do not know that the plants they have are invasive, because they have not looked. There are also those that care not that the plants they have are invasive. Often, after Purple Loosestrife was listed as an invasive plant, people would say "I don't care, I like they looks of that plant."
I'd not be afraid of telling someone that what they offer is an invasive species that should not be traded.

I grow purple loosestrife, and cut it back before it reseeds. I'd NEVER offer it up for trade, LOL. I do grow Dames Rocket, but state on my trade page that I will not send it to CO, where I believe it's illegal.

But, the person offering may not be aware of it being an invasive species.

I myself wouldn't be offended if someone informed me of something being listed as noxious or invasive that's on my trade list. I'm sure alot of people don't know what's considered noxious, invasive or illegal to grow in their own back yards. I'm just as clueless as the next person, and admit to not knowing what I shouldn't grow...

Research has found that Purple Loosestrife will cross pollinate with other members of this family and produce plants that are as aggressive as the Purple Loosestrife. Since this plant also spreads by roots, simply cutting the flowers off before they produce seed is not enough to control this very invasive species.
Every state Ag Department and the USDA as well as the US Forest Service, have asked eveyone growing this highly invasive plant species to destroy it.

tracey nj, I hope you realize that purple loosestrife is choking out wetlands and wreaking havoc with the environment.

It's a major, major, problem, and as another poster pointed out, even if it's not going to seed it can still be cross pollinating and contributing to the problem.

There's a house in our neighborhood that is intentionally growing Japanese Knotweed as a foundation plant, and every time I drive by I wonder what on earth they are thinking.

I planted honeysuckle when I knew it was invasive because I love the smell. It took 15 years for me to be sorry. I don't think it hurts to tell your own experience with the plant. There are invasive plants that you can't be silent about. I personally don't think sweet rocket compares to musk thistle, but it may be a big problem in some areas. Here is the one that gets me upset. Cinnamon vine