I am also shocked by the (luckily few) posters claiming Thomas Markle should "not be denied his right" to see his grandchildren. He's threatened to "sue" Meghan and Harry, no doubt funded by the British media, rubbing their hands at the prospect.
Let him!
If family courts in the US are anything like the UK, the case will be decided based on the best interests of the children, Prince Archie and Princess Lili.
Now let's examine what arguments Thomas Markle and his children can put forward to persuade a judge to grant them access against the will of the children's parents. Let's also think about what safeguarding arguments Child Protective Services social workers will put forward, regarding the risks of exposing the children to Thomas Markle, Samantha Markle and Thomas Markle Junior, what they will likely say to these children and the impact this will have on them, what they will likely do with any pictures and videos taken, what they will say about these children in TV interviews, Thomas Markle's vile YouTube channel, Samantha Markle's next ridiculous book, their twitter posts etc etc.
It's a no-brainer: Thomas Markle isn't suing because it's obvious the only thing he'll end up with is a restraining order against him.
This isn't just about Meghan refusing him access. Any child protection professional or family court judge worth their salt can see that this would not be in the children's best interests.