Unfortunately this is an artifact based on how the outline is created. It tests your texture at 8 locations which will cause these patterns at sharp-angled corners < 90 degrees. The solutions below are not perfect, but will improve the situation:
Solution 1 - Using mip maps:
You can enable Generate Mip Maps at the texture in the Texture Import settings in the Inspector.
Then at the outline material you can adjust Advance - Outline Mip Level until you are happy with the outline shape.
Solution 2 - Painting a very transparent border:
Paint under any sharp corners with minimum opacity (e.g. 1 / 255) which is barely noticable, so that the resulting corner is >= 90 degrees. Alternativaly, you can also add a very transparent rounded border around your image whole image via e.g. a Stroke effect in Photoshop, where you want the outline to be painted.
Then at the outline material, reduce the outline width to a small value, and set the Advanced - Outline Threshold value below the painted value, e.g. to 0.001.
