The half-sister of your granddaughter's half-sister is your granddaughter, or is not related to you.

If your half-brother has a full sister, she is your half sister.

If your half brother has a half sister, she may be your full sister, or she may not be related to you at all.

You grandmother's half-sister is your half-grandaunt.

You have no blood line relation, You don't share DNA whatsoever.

In this scenario putting an example; you and your half-sister share, let's say, the same father but not the same mother and your half-sister's half-sister share the same mother but not the same father.

There is no shared DNA between you and your half-sister's half-sister.

King Tuts wife was his half-sister.