la he

Hola William

Those are the direct object pronouns la/ las (it, her, them), feminine singular and plural. 

They are placed in front of the whole verbal structure when the verb is conjugated:

For example:

I love María - Amo a María 

I love her - La amo

In the examples you've seen in that lesson you have "la he..." "las he..." because the verb is conjugated in the present perfect, so the la/las are in front of the verbal structure: 

La he redecorado toda.

I have redecorated it all.

Las he recogido todas.

I have picked them all.

Here are two lessons on the direct object pronouns and their position so you can see it with detail and more explanations:

Direct object pronouns

Position of pronouns with conjugated verbs

I hope it helps.

Saludos 

Inma