IANAL, but I read legal blogs a lot

People confuse copyright law and trademark law, but they're actually quite different areas of law.
Copyright law is intended to protect creative works. Clearly there is no issue with copyrights; it's obvious that neither image is a copy or even adaptation of the other.
Trademark law is not intended to protect the owner of the trademark at all. Its purpose is to protect
the consumer.
The rules about uniqueness of trademarks are set up with the intent to keep consumers from mistaking one product or brand for another. Thus, it's OK for the name "Apple" to be in use by both Apple Computers and Apple Music (the publisher of the Beatles' stuff): nobody is going to pick up a Mac and wonder if it's a new Beatles recording. Similarly, there might be a "Moe's Bar" in Springfield and another in New York; the geographical difference makes mistaking one with the other impossible. Unfortunately in our situation, there does seem to be some proximity in terms of the product, so there could be confusion.
I don't know what the trademark analog of copyright's "prior art" is, or if such a concept even exists. Clearly DC's "Cody" was well-established before this other bird came on the scene. But with trademarks, maybe that's not enough. Maybe you actually need to register the image, I don't know.
Here is some
information about trademarks. But you're probably better off talking to a professional.
I did a search for the trademark "Twitpay" and found nothing. Also, their logo has an "SM" next to it, indicating that it's a "service mark", i.e., a trademark for services. Note that it doesn't have an "(R)" next to it. That indicates to me that it's not a
registered service mark. Perhaps the thing to do is to send a registration request for Cody to the USPTO straightaway, and preempt any argument.