My parent's are in US on visitor VISA and they can stay here until August 20th, which is the end of six month.Since they are eligible, they are planning to apply for TPS status in couple of days. If the case is still pending until 20th of August (assuming it gets approved after this date) and they continue to stay here without applying for visitor visa extension, is this visitor visa still valid in the future upon TPS designation for Nepal is removed by USCIS?. Their visa is valid until 2020 and I am aware the benefeciary will move back to previous status if USCIS does not renew TPS designation.

If you don't file TPS-EAD, i believe their visa should be valid till its expiry date.

I think anyone visiting in business visa can not stay here more than 6 months in one trip . For some reason, I feel vistor visa is same as well. If you extend that stay, that would be additional 6 months, but no more than that. Which means, it can be at max 1 year of stay if the extension is applied . If they file TPS and extend the stay, that 6 months stay will be violated ( if extended i-94 date, that would be 1 year), hence the whole multiple entry visa will be invalid.
So I think, if they file TPS and stay here beyond the date on i-94 , that will invalidate their visitor visa that is valid till 2020. To come back to any visa from TPS, that visa has to be maintained the whole time, so I doubt if they can come back to visitor visa again without reapplying again.
If you are not planning to apply for EAD for your parents, its not worth to apply TPS for sure.
I think you should see some lawyer before you make this decision.