Can hyaluronic acid or hyaluronidase cause under eyes damages and treatment? Treatment options? (photos)

You state that you had a hyaluronic acid filler treatment about 16 months ago. Then in December of 2019, you had the filler removed with enzyme and you had fat transfer 2 weeks later. Now you are 6 months out from your procedure but are increasingly concerned about discoloration in the right lower eyelid that you first noticed sometime in February. It is probable that some of the change you are aware of could be related to hyaluronic acid. It is inappropriate to characterize it as damage. You have also had a surgical procedure on the eyelid which may also be the basis for the color change. Given how common it is for surgeons to under treat with enzyme, it is worth flooding the eyelid with hyaluronidase to see if any change occurs. However, if the area does not respond to a large enzyme treatment, then one must presume the effect is from the fat procedure. A detailed examination is helpful to confirm this impression. 

you look like you have normal aging. hyaluronidase cannot damage normal skin or tissue. id suggest a lower bleph for you, fillers, and peels. I would start our eye rolling protocol (see link).
at home peels like cosmelan, enlighten and aerify along with dermarolling (MTS roller with anteage MD ampules weekly from emeragecosmetics.com see eye rolling package for weekly treatment) should be started now.  visit emeragecosmetics.com where we ship medical grade skincare all over the world AND do free virtual skincare consults daily. Proceeds benefit BLM and LGBTQ+ charities/organizations.
There are many things you can do to treat under eye hollows and dark circles. A surgical option to remove skin and/or fat will be the best long term.  However, non invasive less downtime options such as fillers, lasers, microneedling/PRP, cosmelan peels and stem cells can all help give some improvement. I suggest. You get a formal consultation to see what is best for you and your goals.  Best, Dr. Emer.

Thanks for reaching out. You are not alone. I have seen similar sad things happen to other patients who came to me for a consult on how to treat the hyperpigmentation and hollowing and/or irregularities in contour under the eye.
It appears to me from your pictures that you have post-inflammatory hyperpigmentation in that right lower lid, and/or iron staining (from bleeding) in that area....both of which can occur with procedures performed in that area. In either case, I would recommend starting with treatment of the hyperpigmentation with creams, such as Melanage Cream with Arbutase LC (from Young Pharmacy of Wethersville, CT) or 4% hydroquinone cream, being careful not to get any into the eye. It may take 2-4months to get it to resolve (one skin cycle is about 2 months). I recommend you avoid other procedures till the hyperpigmentation is under control. Anything that involves needles or cutting could potentially worsen the problem you already have.
After the pigmentation problem is resolved (or nearly-resolved), I would consider treatment with a bio-stimulatory agent injected via a cannula to fill in the defect and improve the texture of the skin.