"She sends this."
Translation:היא שולחת את זה.
In Biblical Hebrew את wasn't obligatory. While in Modern Hebrew it is almost always obligatory, in this case (before זאת meaning "this" in general), it is formal Hebrew, so for some reason it sounds better to Hebrew speakers without את.
It's not that it's "added" in Modern Hebrew, it always existed in Ancient Hebrew but seemingly wasn't obligatory.
modern hebrew basically needs every verb to have something connecting it to its direct object, so for verbs where there isn't a specific preposition you use et.
You ask about את זאת but in the phrase it reads את זה. Is hat just a mistake or do you have a specific reason?
This is הזה when it's describing something:
This book - הספר הזה
When it's on its own it's simply זה.
In colloquial Hebrew you can hear things like תני לי את הזה, give me that one. It's kind of an abbreviation of whatever the thing is: תני לי את (הספר) הזה.
But don't worry about that for now, just focus on the first part.