Depends on what is in the product.
More importantly, it depends on all the products that have been used for the last 20 years.
You
should assume that their stuff is going to contain clopyralid (half life of 11 years) and tordon (half life of 7 years) (I cannot remember the persistent component in tordon, so I've gotten into the bad habit of just using the commercial name).
Clopyralid is what has shut down loads of composting operations. They would take in grass clippings which would taint all of the
compost and then if any compost is used in a garden, all (or nearly all) of the garden would die. Thus putting the composting operation out of business.
I suppose that something from
fungi perfecti would save the day. Those guys are amazing. At the same time, I wonder if they did have something, is it commercially available yet? It would be cool to ask one of their folks to chime in here.
If they still have weeds coming up in their grass, one might speculation that the pesticides have dwindled to the point that they are no longer potent. To that I say:
1) No longer potent for some plants, but not all.
2) While it might not kill plants in your garden at this time, it could make them less happy than if you just didn't use compost made from those clippings.
If I were in your shoes, I would suggest that the mow high enough and frequently enough so that the grass clippings wouldn't mat - so let the clippings stay in the grass. Keep the clopyralid and tordon out in there grass where it will do the most good - continuing to give the grass an edge over the broadleaf plants in the area. In fact, those clipped grass blades contain the perfect stuff for feeding grass, and their grass blades also contain the herbicides of many years gone by. By mulching their own grass, they will greatly reduce their need for fertilizer and herbicides. And, of
course, by mowing high they will reduce their need of herbicides, fertilizer and
water.