Mechanical royalties are payment for the right to cover or reinterpret a composition (which includes music or a song) - either by written sheet music or your own recording of that composition. Typically, if you wanted to get a mechanical license to cover or reinterpret a composition, you would go to the Harry Fox Agency website and pay a fee (most often $15 for an average song), and they would issue you a compulsory mechanical license allowing you to perform your work. Thus, your statement means that the "Company" is not going to pay that $15 (or whatever it is depending on the song) - meaning that someone else, could be you dependant on your situation, must pay that compulsory mechanical license fee (i.e. mechanical royalty). If you are giving another company some songs in which you covered, then the company is saying that they are not going to pay for that fee (which means you could have to).