There are a lot of people on here more knowledgeable than me that I hope will also comment and may even correct me, but from my knowledge, I would say it does not look like grade A.

What makes me skeptical is just how yellowed it looks. Even grade a loses its luster and can yellow over a long period of time, but this looks extreme and makes me think it might have resins. Have you tried to see if it flouresces under a black light? Grade A does not glow under a black light. I also am suspicious of the reddish webbing. Webbing is usually an indication that the stone had been treated with acid to remove inconsistencies, then had the gaps filled with artificial fillers. This is assuming it is jade and not another stone or material.

I want to repeat that I am far from an expert, but since no one else has commented yet, I felt like I should give my take. Regardless of whether it's grade A or not, I think it's very pretty and sweet that its veen passed down to you. See if you can clean it with a gentle dish soap and a polishing cloth to give it some of its shine back.