Word Choice

They are both acceptable. I'd likely go with the first.

The repairs were completed by the owner.

The repairs have already been completed by the owner.

Neither of these sentences say that you don't need to do any more work. The say the repairs have been completed by the owner. But the
owner did not do any of the work. He hired you to do it.

Are you a contractor and the owner is your customer? Then you can say:

As directed by the owner, the work is now completed.

or

The work contracted by the owner is now completed.

or


The company hired by the owner has completed the work.

That's an assumption.