Documenting the infringement is trivial. You could go to a notary with a computer for example, have them print the image from the competitors site and mark it with the date and time as well as recording the information in their notary book. If it ever goes to trial you could simply subpoena them to testify (and pay their expenses to do so).
Does your competitor run their own website in-house or do they use a third party hoster? If they do-not self-host have you sent the hoster a DCMA take-down notice? See How to Send a DMCA Takedown Notice
Specifically, your notification must:
• Be in writing; • Be signed by the copyright owner or agent; your
electronic signature is OK; • Identify the copyrighted work that you
claim has been infringed (or a list of infringements from the same
site); • Identify the material that is infringing your work; • Include
your contact info; • State that you are complaining in “good faith;” •
State that, “under penalty of perjury, that the information contained
in the notification is accurate;” and
• State that you have the right to proceed (because you are the
copyright owner or the owner’s agent).