On feature services there is the 'extract' capability. However, even disabling the option, users are able to download data from third-part softwares like QGIS.
Steps to reproduce:
The Bug BUG-000089531 describes a similar behavior on ArcGIS Desktop:
Be unable to extract data is very important for govenance strategies.
This setting seems to prevent ArcGIS Pro from exporting the data. Because this is a feature service, it is sending geometry and attribute data, which other programs such as QGIS are able to save to local files/features if there is code that allows it. If you really want to to make it more difficult to download the data, only offer Map Image service if you can and you do not require feature capability.
If you don't want users to access your data (i.e., via extraction), consider securing your services. This product documentation on ArcGIS Enterprise and standalone ArcGIS Server may be of help.
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