That is not going to be from a burrowing insect (unless you live on a 'Dune' like planet) but rather a burrowing mammal; e.g. mole, vole, etc.
If you allow it to stay you are going to get a lot more of these strange piles of dirt. If they have taken up residence then a lot more. Probably more than you would care to put up with.
First off, a very effective deterrent is sprinkling used cat litter around every opening (aka 'strange-looking pile of dirt') that you can find. If you do not have an in-door cat then I'm sure one of your neighbours will and they will very likely be more than happy to have you empty a litter box or two for them.
btw, on the subject of neighbours: you may want to proactively alert your neighbours about this. If you use a non-lethal eradication method like used kitty litter then the burrowing rodents are going to set up shop somewhere close by. Alerting your neighbours now will save a possibly embarrassing conversation later. <them:> Darn it! I've just got a bunch of burrowing rodents in my lawn! <you:> That's strange. I had a bunch last week but got rid of them!
My second point is in regard to the long term health of your lawn. The burrowing mammal(s) has chosen to make a home there for a reason. It is very likely that your lawn contains insect grubs or other tasty morsels that have attracted it/them in the first place. Get rid of the problem at the source that is attracting them and they won't come back in the future.