1. Why are they pushing back on it? Have you asked them what they consider up to standard? If they don't have high enough code standards and think it's OK to push crap, then there is a clear expectation gap that you should identify to them and tell them they are not meeting the bar.
2. Did they have any say in these standards? Sometimes you can turn an enemy into an asset simply by having them own a piece of the standard (and holding them accountable if that standard doesn't hold up)
3. What do they suggest in lieu? Maybe it's a stylistic thing, maybe it's a quality thing. Maybe they don't understand the difference, or maybe their impostor syndrome is making them defensive.
My summary is that you need to ask probing questions to fully understand their perspective. THis is difficult because they sound defensive, which is reasonable - your approach sounds a little like an attack due to your frustration. I can assure you they are frustrated as well!
Finally, keep in mind to set up the right context. When the light is red, stop pushing. Find a way to have an open and constructive dialog - you will have to bear that responsibility, but once you can find that, you will probably have better luck.
And document each of these steps, in email, to the person. Then when you go to leadership, you can share what you've done. If they ultimately just don't meet the bar or expectations, they should be let go.