Agree. I'd pretty much ignore them or pluck them out when you feel like it. I'd be more concerned whether there is remaining larger trunk type roots. Do these little sprouts grow in a straight line? I might take the pointy end of a pick axe and see if I can dig under and lift out any remaining larger roots. If they are still there they will decay over the years and will depress the lawn at those spots.

You could use a broad-leaf herbicide, like you would for lawn weeds, that won't hurt the grass. Might not stop them completely until the stump runs out of gas. Mowing is a good way to deal with them.

put a stump killer in the very expensive applicator at this link...

when you find one.. snip it clean to the ground... and apply one drop of stump killer ..

sooner or later you will kill the HUGE root mass that is refusing to die .. not only from the killer.. but by continually removing green food making leaves ... there is a lot of stored energy down there ...

undiluted round up is labeled as a stump killer ...

this is not a spray thing ... unless you want nice big brown spots all over you former lawn .. lol ..

ken

do not store near the hotdogs... mark accordingly.. or even better.. put unused product back into the properly labeled container ....the key is the precise ability to apply one drop [more drops or the entire green rim on larger stumps.. the cambian layer ].. no wind drift .. and if it falls over.. it doest all run out ...

https://www.google.com/search?q=plochmans+mustard&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a&um=1&ie=UTF-8&hl=en&tbm=isch&source=og&sa=N&tab=wi&ei=XQTcUYCCC_OFyQGCg4DAAg&biw=1154&bih=805&sei=XwTcUbmZHZK4yAHD0oDYDw

https://duckduckgo.com/?q=cambian+layer&t=ffcm&iax=images&ia=images

Thanks for the responses. Mowing over them is not enough, some of the leaves remain and the shoots continue to grow. So far, I've been plucking them but it seems they are increasing in number, so that strategy would be definitely long term, if ever. I'm actually doing the cheapo version of what ken_adrian suggests- I have a plastic shield that goes around the stem and I'm using concentrated Roundup as the nectar of choice, dabbing it on with a small rag. I hope it's to die for!

I was just wondering if there is another strategy I had't thought of. The root that generates the shoot is so close to the surface, I thought about cutting a slit along it for access, then cutting it off and applying Roundup to the cut. (Yes, I'm using the broadleaf formulation)

2 things... 1) as a former chemical engineer who currently works in the food business, putting Roundup in a mustard bottle is an extremely, extremely NOT OK thing to do. I know Ken was just using an example, but DO NOT do this!! lol OK? 2) Why not try to rip up the roots with a pick axe rather than doing it chemically? I had to do this many years ago when we had a maple tree removed. You may be surprised at what you dig up and it will be gone in a day rather than a potentially a very long time.

When we moved into our home I had two enormous trees taken out of the front yard and the stumps ground out properly. They produced root shoots for years- I just went out daily with pruning shears and cut them to the ground.

Eventually the roots run out of nutrition and it stops but you have to stave them thoroughly by eliminating all the food producing leaves every day- any leaf that sees sunlight makes food and extends the problem by nourishing the roots. How long you have to do this depends on the tree and how well fed the roots are/were. Just keep at it, be vigilant daily, and they will run out of steam in time.

Again my thanks to all who responded. To danielj, as mentioned I thought of trying to get at the roots by making a slice in the turf over them. If I can fold the sides of the slice back, there will be less repair work to the lawn.

Yeah, if the gentle method doesn't work I'd bite the bullet and dig around until you find the roots that you might be able to rip out by hand. Your lawn will regrow quickly enough or you can reseed as needed in the fall if you don't have a spreading grass like KBG. That way you'll be done with it.

I had a lot of them, and the mower pretty much took care of them over time. Biggest problem was in areas the mower couldn’t go.

Use a paint brush and paint the leaves of the shoot with roundup. grass is generally not disturbed

Where do these morons come from, who bump old threads that have no business being bumped!?!?!?! Gardenweb/Houzz needs to introduce a some kind of 'lock' that you can only bump an old thread if you've had 10 other posts, and have been registered for 3 months!!!

Firstly, if the main tree is gone as was the case for the OP, you should just keep driving the lawn mower over the shoots. They will die eventually. THIS WAS ALREADY CONFIRMED BY MULTIPLE PARTICIPANTS IN THE DISCUSSION. This is why I don't bother to spray tree seedlings in my lawn. You only need to spray things WITH A SELECTIVE (i.e., not roundup) that are adopted to maturing and sexually reproducing in lawns, like violet.

But, if you were still going to spray distant, spreading suckers and shoots of a weedy tree, at all, you'd use something other than roundup! Much easier that all the tedium of trying to avoid hitting your grass with a non-selective like roundup/glyphosate. Personally, I'd use [generic] Crossbow at the times of year it's appropriate to use.