On the passing of his grandfather, I sent him a bouquet of flowers and a condolence card.

The correct option is Away.

This question tests the correct usage of phrasal verbs in English grammar, specifically referring to the death of a person.

The phrase "passing _______" needs to be completed with a preposition to form a phrasal verb that means "to die".
The phrasal verb "pass away" is a common, polite euphemism used in English to mean "to die". Therefore, when referring to the death of his grandfather, we say "the passing away of his grandfather".

Let's examine why the other options are incorrect in this context:
- "Passing over" can mean to ignore or bypass someone for a promotion or opportunity.
- "Passing into" means transitioning or changing into another state or form.
- "Passing by" means going past something or someone physically.
None of these options convey the meaning of dying, making "Away" the only appropriate and grammatically correct choice to complete the sentence.