The role of the gerund
Gerunds have an ambiguous part of speech. Within their own local phrase they are verbs, but outside that phrase they behave as nouns.
In your example, "phoning" is head of the noun phrase "phoning her", which in turn is object of the understood preposition "from". Yet within the phrase "phoning her", "phoning" is a verb with the direct object "her". (Nouns don't allow direct objects.)
Your main verb in the second half of the conditional is would save. That verb is transitive here, but its direct object is not me! Rather me is the indirect object, and its direct object is the entire nonfinite verb phrase phoning her, where her is in turn the direct object of the verb phoning.
In other words, the apodosis (the “then” part, a finite clause) of your conditional works out like this:
- SUBJECT: that
- TRANSITIVE VERB: would save
- INDIRECT OBJECT: me
- DIRECT OBJECT: phoning her
- TRANSITIVE VERB: phoning
- DIRECT OBJECT: her
This is the sense of save given by the OED’s sense 18 a:
a. transitive.
To avoid spending or consuming (money, goods, etc.); to make a saving of (a given amount), esp. on a purchase.
Also with indirect object (formerly also with †to): to enable a person to avoid spending or consuming (money, goods, etc.).
They provide an old citation from 1539 (in Late Middle English transitioning to Early Modern English) for the obsolete use with to they mention:
- 1539 William Arthur Jobson Archbold The Somerset Religious Houses (1892) 73
Ther will be a great soome of money that shalbe salved to the kinges highnes therbye.
Nowadays we would not say that a great sum of money shall be saved to his highness. Instead, under dative alternation we would say that something or other would save the king a great deal of money.
So your me is the person benefiting from the action of saving, or at least of avoiding spending. It allows them to avoid spending or using something, just as it does when you ask somebody to please save you a piece of pie for later.
Again, phoning is the head of the nonfinite verb clause phoning her, so that the grammatical role that phoning is fulfilling here. It’s that clause’s verb.
But the entire clause phoning her is the direct object of save, and me is that verb’s indirect object.
Saving me some pie and saving me phoning her are the same structure. They each have a noun phrase as their direct object.