1. Check Statement (I): "Viscosity of gases is greater than that of liquids."

   • In general, liquids have much larger viscosity than gases.
   • Example: water has much higher viscosity than air.
   • So the statement that gases have greater viscosity than liquids is false.

   Therefore, Statement (I) is incorrect.

2. Check Statement (II): "Surface tension of a liquid decreases due to the presence of insoluble impurities."

   • Surface tension depends on the nature of molecules present at the surface.
   • Insoluble impurities such as oil spread over the liquid surface and generally reduce the cohesive force at the surface, thereby decreasing surface tension.
   • Hence this statement is true.

   Therefore, Statement (II) is correct.

3. Match with options:

   • A: Statement I correct, Statement II incorrect ❌
   • B: Statement I incorrect, Statement II correct ✅
   • C: Both incorrect ❌
   • D: Both correct ❌

Therefore, the correct option is:

$\boxed{\text{B}}$