Like Jon I do not think this is marketing.
Provided you respect any known opt-outs / objections and have such use properly covered in your privacy notice, I don't think there is a specific DP objection other than - is it fair? That may depend on exactly what you said in the original letter and how much the low response would hamper the study.
If it was me I would actually refer to my CG for a decision on this - looks more like a Caldicott issue than a DP one. CG is there to take the patient view
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