Learn English – Is this sentence grammatically wrong? (Using as)

The word 'then' has many meanings. In some of its meanings, it is perfectly grammatical at the end of a sentence.

For instance, from definition 3.b from the Merriam-Webster online dictionary (here)

3.b: according to that : as may be inferred. 'your mind is made up, then?'

Another example is using this meaning (here):

1: At that time. 'Come at noon; I'll be ready then.'

The Macmillan dictionary describes the meaning of the OP's question directly:

3.b: As a result. (SPOKEN, used at the end of a question when you think something must be true because of what has just been said.)

"We went to the same school." "You're old friends then?"

You're not angry with me, then?

This last one was the meaning of 'then' in the OP's post.

Person C means "As a result of what you just told me, I conclude that 'you both are really lucky'."

Definitions

no matter - (adv) regardless of

whether - (conj) expressing a doubt or choice between alternatives

Explanation

No matter emphasizes that which option you choose is not important.

Whether informs the listener that multiple options are about to be presented.

Examples

The conclusion holds true no matter whether the proof is carried out through this formulation or that formulation. - Has emphasis from no matter

The conclusion holds true whether the proof is carried out through this formulation or that formulation. - Does not have emphasis from no matter

The conclusion holds true no matter the proof is carried out through this formulation or that formulation. - You can't say this. It is grammatically incorrect.