Έχοντας τελειώσει την τηλεδιάσκεψη, κοίταξα την αναπάντητη κλήση της μαμάς μου και την πήρα αμέσως πίσω.

It is an introductory phrase meaning having finished or after finishing.

Grammatically, it works like an adverbial participial expression: it tells you what happened before the main actions. So the sequence is:

1. I finished the teleconference.
2. I looked at the missed call.
3. I called my mom back.

So Έχοντας τελειώσει την τηλεδιάσκεψη sets the background for the rest of the sentence.

Because Έχοντας τελειώσει makes the idea of completion first very clear.

• τελειώνοντας can mean something like while finishing, as I was finishing, or when finishing
• έχοντας τελειώσει is closer to having finished / after I had finished

So in this sentence, έχοντας τελειώσει emphasizes that the teleconference was already over before the speaker checked the missed call.

The subject is the same as the subject of the main verbs: I.

Greek often leaves subject pronouns unstated because the verb ending already shows the person. Here:

• κοίταξα = I looked
• πήρα = I called / I took

So the sentence naturally means Having finished..., I looked... and I called back...

They are in the aorist because the sentence describes completed actions in sequence.

• κοίταξα = I looked
• πήρα = I called / took

The aorist is very common in narration when you list one finished action after another. In this sentence, the speaker is telling a short chain of events, so the aorist is the natural choice.

Because την is the feminine singular accusative form of the definite article, and both nouns are feminine singular direct objects.

• η τηλεδιάσκεψη → την τηλεδιάσκεψη
• η κλήση → την κλήση

So this is simply Greek grammar: the direct object takes the accusative, and the article changes form too.

It literally means unanswered call, and in normal English that is usually missed call.

• κλήση = call
• αναπάντητη = unanswered

This is the standard phrase you would see on a phone for a missed call. The adjective αναπάντητη agrees with κλήση in gender, number, and case.

Because Greek uses the genitive to show possession.

• η μαμά μου = my mom
• της μαμάς μου = of my mom / my mom’s

In the sentence, the missed call belongs to the mom, so Greek says the missed call of my mom = my mom’s missed call.

Also note:

• μαμάς is the genitive singular form of μαμά
• μου means my

Here την refers to my mom—not to the call.

So the idea is:

• I saw my mom’s missed call
• I called her right back

That is why την πήρα πίσω means I called her back. Greek is happy to use the pronoun once the person is obvious from context.

Literally, παίρνω πίσω can mean take back, but in this context it is an idiomatic everyday way to say call someone back.

Context is everything here. Since the sentence is about a missed call, the natural meaning is:

• την πήρα πίσω = I called her back

So this is not about physically taking someone back; it is about returning a phone call.

Because weak object pronouns in Greek usually come before a finite verb.

So:

• την πήρα = I called her
• τον είδα = I saw him
• το έκανα = I did it

This is normal Greek word order for clitic object pronouns in statements.

Αμέσως means immediately or right away.

So την πήρα αμέσως πίσω means I called her back immediately / right back.

It adds the idea that the speaker did not wait. In English, right back often gives the same feeling.

Yes. Greek word order is more flexible than English, although some patterns are more natural than others.

For example, you could also hear:

• Την πήρα πίσω αμέσως
• Αμέσως την πήρα πίσω

The exact emphasis changes a little, but the meaning stays basically the same. The pronoun την would still normally stay before the verb.

Because the sentence begins with an introductory participial phrase:

Έχοντας τελειώσει την τηλεδιάσκεψη, ...

The comma separates that opening background action from the main clause. This is very similar to English punctuation in a sentence like:

Having finished the teleconference, I looked at the missed call...

Not necessarily. Here κοίταξα is better understood as looked at or checked.

In phone-related context, it can mean that the speaker looked at the notification or checked the missed call on the screen. So it sounds natural, not strange.

If the sentence had είδα, that would be more like I saw / noticed. κοίταξα suggests a more deliberate look.