Whether an online converter keeps your files depends entirely on how it works. A browser-based (client-side) converter never receives your file in the first place, so there's nothing to keep. A server-based converter does store your file temporarily to process it — reputable ones delete it within minutes to hours, but you're trusting them to do so.
The two models, and what each keeps
A client-side converter runs in your browser and never uploads the file, so there is literally nothing on anyone's server to keep. A server-side converter has to receive your file to convert it, so a copy sits on the company's machine at least briefly — and what happens to it next is entirely down to their policy.
How long do server-based converters keep files?
It varies. Good services auto-delete within an hour or a few hours and say so plainly in their privacy policy. Others keep files longer, are vague about it, or reserve the right to use uploads to "improve their service" — that's the risk. Always look for a stated deletion window before uploading anything you care about.
How can you be sure a converter isn't keeping your file?
The only way to be certain is to use a tool that never uploads it. If the conversion happens in your browser, there's no copy on anyone's server to keep, delete, leak, or train on — the privacy is structural, not a promise. You can confirm it by turning off Wi-Fi after the page loads, or by watching your browser's Network tab during a conversion.
What about File Transmute?
Most File Transmute tools convert in your browser, so your file is never uploaded and there's nothing to keep — a live panel shows 0 bytes sent. The few server-based tools (clearly labeled) delete your file right after converting. Try a fully-local tool like Compress PDF or Protect PDF, or read is it safe to use an online file converter.