TexOne collects nothing.
It contains no analytics, no crash reporting, no advertising identifier and no third-party SDK. It makes no network requests of any kind — there is no network code in it to make one. The typesetting engine runs inside the app's own process, and every font, package and format file it needs ships inside the app.
Your documents — the LaTeX you write, the Word files you import, the PDFs the engine produces — stay in the files you keep them in, on your device or in locations you choose. Nothing you type and nothing the engine typesets is transmitted anywhere, because there is nowhere for it to go.
Your preferences, on your device, using the standard mechanism the operating system provides for exactly that. Deleting the app deletes them.
Write to softwareone.support@gmail.com.