That's actually a difficult question. 2.4D is not real persistent in soil. In the soil, it has a half life of 16 days or less (depending on soil type, conditions etc), meaning in a month about 3/4 of it would be gone.
However, it is taken up by the plants, so it will be IN the grass. Horses and cattle have been killed by eating forage treated with 2.4D. I think once it is taken up by the grass, it stays there until the grass decomposes, at which point it will be released in to the environment to begin its break down process:
"2,4-D residues taken up by plants remain intact in the foliage until it is lost as litter and degraded in soils (Newton et al. 1990). Fruits from treated trees have been found to retain 2,4-D residues for up to seven weeks (Love & Donnelly 1976, in Que Hee & Sutherland 1981).
https://www.invasive.org/gist/products/h ... 0.24-d.pdf
So the residue that is on the surface should be gone within a couple months. The part that the grass absorbed will be there until the grass decomposes and then will be released in to the environment and then will breakdown as it is exposed to sun and water, over a period of probably 1-2 months, again depending on conditions.
Personally, I wouldn't use them on my veggie gardens. And since it is an herbicide, it could even be damaging to ornamental gardens.