I'm no kind of lawyer, but I do occasionally have to make a judgement about copyright issues, usually to informally advise artists about how to protect themselves and less usually to warn them when they might be breaking someone else's copyright.

Example: an artist that I produce fine art prints for does celebrity portraits. No way they'd get the celeb to sit for them, so they collect a dozen or so photos of a celeb and use those to paint an impression of the celeb: no problem there, they're not directly copying anything. But recently, when Prince died unexpectedly, they needed to produce a portrait in a hurry. They found a photo - one single photo - online and copied it, albeit in paint. They weren't happy when I suggested that they were leaving themselves open to a copyright claim. Yes, they'd used skill and effort to produce their work, but it would be hard to convince anyone that it wasn't 100% based on that photo.

At the risk of stating the obvious: if you copy a creative work that is still within copyright, you are infringing the rights of the owner. It doesn't sound like you can claim that any of the usual exceptions apply (non-commercial research, review, parody, educational use) so I'd comply with their take-down requests promptly.

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