My question is: Why were the child's grandparents at the park while you were watching them?? Spying?? And my first thought I "You know how grandparents are". Both my parents and ESPECIALLY my inlaws are insane helicopters with my kids and it drives me bonkers. Just because THEY would have rushed over and hovered, doesn't mean that that's your style. I, too, let little ones wander and explore but always within my sight. And kids that age are constantly putting things in their mouths, do the grandparents not know this?
It sounds like the parents heard what the grandparents had to say and just wanted to raise the concern with you to hear your side of the story before making assumptions. And it sounds like they have sided with you, because if they believed their child was unsafe then there is no doubt they would be issuing notice.
That being said, I would have a huge issue with feeling like I couldn't go out anywhere without the grandparents spying and making judgments. And I don't think I could let it go without raising the issue myself. I would say something like. "Thank you for meeting with me, and discussing the concerns you had about _____ safety in my care. Health and safety is, and always has been my number one priority when it it comes to the children in my care. That being said, I can't shake the uneasy feeling that whenever we venture out for fun activities away from the house I will be spied on and judged for my actions as nobody wants to feel this way while working. If your parents are out and about while I am also out with the children, please have them come over and introduce themselves so we can also get to know each other. Thank you and have a great day!"