My husband's grandparents quitclaim deeded a vacant piece of land to him last year. We are interested in selling the property now. What sort of tax implications will we encounter? Is it possible to quitclaim deed it back to them and let them sell it?

What state are you in? The tax question may be what is the basis for the property when you acquired it. That may be its value on the date acquired. I'm not sure. Then you would have tax obligation probably as a capital gain. Difference between sale price (less costs of sale) and acquisition price.

You always need to consider whether the QCD was done properly and also make sure there are not liens and encumberances on the property. This shouldn't be that expensive of a legal question for you to spend money with a lawyer getting your answers.