Transform > Reflect is Distorting My Shape

I purchased a stock Illustrator file from Adobe Stock. The image is symmetrical and looks fine on Adobe's website, but one part of it is distorted in the Illustrator file that I downloaded. I tried to fix the distortion on the left by copying the correct part on the right and using the Transform > Reflect functionality in Illustrator to flip the shape and use it to replace the distorted part of the image. However, whenever I Reflect the right side of the image to the left side, it distorts again, as you can see on the left-side of the image below.

What might be causing Illustrator to screw up the path here and distort the shape during the Reflect process? Any ideas on how to fix this?