Warmaster Horus
Explorer
You keep talking about the grapple attempt as if the dragon's claw is guaranteed to hit you any time it tries, and the only question is whether you can physically wrestle the beast into submission.
No, I'm talking about the rules for Grappling.
Using at least one free hand, you try to seize the target by making a grapple check, a Strength (Athletics) check contested by the target’s Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). If you succeed, you subject the target to the grappled condition (see appendix A).
In the case I'm thinking about, a Huge size creature trying to Grapple a Medium size creature, I'd probably assess a Disadvantage to the Medium size creature's Strength or Dex check. This is based on the wording that to initiate a grapple your target can only be one size class larger than you (no restriction on smaller). Given that, my assumption is that Medium sized creature is very outclassed by a Huge one. Just how I'd rule it.
That's all I have to say. Peace, Out!