Reporters are human, and like everyone they want to feel appreciated. It’s always a good idea to thank a reporter after an interview and when an article is published. But there is one caveat: If you’re working with a PR agency, let them do the thanking. This will create a degree of separation, which is important for many reasons, including being a buffer if a correction is needed, and so the reporter understands it’s best to call the PR person to request an interview or materials.
The best way to thank a reporter is by emailing a short note. Gifts of any kind are not appropriate and, at many outlets, it is unethical for a reporter to accept one.
Also, it’s a nice touch to remember reporters with a holiday card.