Hi Varada,
As you can see, the demo also uses LayoutTopMenu block and it doesn't raise exceptions on opening the hamburguer menu on phone view. This seems to be the way this screen is implemented, maybe its updating some client variables that feeds the recaptcha, I don't know. Sorry but I don't have time to join on a call, we need to figure it out other way, either replicate this bug in a personal environment and share the module or else I can not help. You just need to replicate the bare minimum widget tree structure of your application, not everything. If the bug doesn't happen on this scenario, then it should be something other than the recaptcha itself.
Regards,
Leandro Rodrigues