Text-matching software (TMS) is a standard part of efforts to prevent and detect plagiarism in upper secondary and higher education. While there are many studies on the potential benefits of using this technology, few studies look into potential unintended side effects. These side effects include students worrying about being accused of plagiarism due to TMS output, even though they did not intentionally plagiarise. Although such worries are frequently mentioned in the literature, little is known about how prevalent they are, why they occur and how students react to them. This paper aims to fill this knowledge gap. The data for the study comprise 36 interviews with upper secondary and Bachelor students from three European countries combined with survey data from 3,424 students from seven European countries representing a broad range of disciplines. The study found that a substantial proportion of the two groups of students -- 47% of upper secondary and 55% of Bachelor students -- had experienced TMS-related worries during their current studies. Furthermore, there were substantial differences across countries. Students worry partly because they have a poor understanding of how TMS is used in their institution, and partly because they know that plagiarism is taken very seriously. The study shows that TMS-related worries can lead students to become very focused on not being caught plagiarising, to such an extent that some adopt citation practices that they believe are suboptimal. The paper concludes that institutions using TMS should always combine it with training for students and teachers. Students should be clearly informed about how TMS is used and should develop an understanding of plagiarism and good citation practice that goes beyond the narrow focus on any overlap between texts elicited by the software.