Return them to your lawn. Clippings contain nitrogen and other nutrients and when returned to the lawn the clippings recycle nutrients in an organic, slow-release form that promotes steady grass growth. Returning clippings reduces the amount of supplemental nitrogen fertilizer required by lawns.
I have some customers who let me mulch clippings but most believe even though I argue that mulching builds thatch and leaves clippings on the lawn. A lot of people believe this and even if I tell them its not true they don't listen
Bagging Grass was an effective way of cutting grass back when it first started back in the fifty's, back when mowers simply cut grass. They argue and believe leaving the clippings contribute to thatch because it did then. The big difference between then and now are the mowers used. There mowers then left clippings of 2 to 4 inches in length depending on the frequency of cut, they (the clippings) laid on top of grass and didn't break down effectively, they didn't contribute anything but problems to a lawn but today with the use of things like micro cut blades, gator blades or some type of mulching blades and vacuum decks our grass clipping can be as little as half an inch and they filter down to the soil and recycle nutrients that promotes steady grass growth which is hard for some to understand but you just do what you know is right.
I know it's sometimes hard to talk to and make the older generation understand some things of today and how far we have come since the fifty's and what's scary for me is at 61 years old is wondering where the next generation is going and how foolish we must look to them.