Former home owner had garden service (on estate sale), new owner did not know and is being charged for 2 months of service. Can they collect their cha

In short, probably not.  You were not in privity of contract with the lawn service.  That being said, if the company performed work on your property, they are likely entitled to some compensation for services rendered.  Additional factors can change this analysis including things like an HOA etc.  For a definitive answer you will need to sit down with an attorney who practices in this area of law to perform an analysis of the circumstances.  Only then will you get an answer you can act on. Best of luck.