hello, you can delete your current private data in the settings menu > privacy. if you open sensitive websites you can do so in a private tab - then they won't appear in your history or the top sites list.

Private Browsing on Firefox for Android

Good tip about private browing but it is a pain to have to select this everytime.

Also. Clear Private Data in Settings does not remove the top sites. It removes some of them but not ones that may have arrived by sync. If I try to remove any of them individually it gets replaced by another one automatically from a history that must be somewhere.

This is not logical. Removal of history should prevent visited sites from appearing in Top Sites.

Whycan't one just disable Top Sites? I don't need it: i have bookmarks.

i'm not sure how sync plays into this issue & what happens to the history data in sync when you delete the private data on the mobile device. do work around that issue, you'd probably have to exclude the history from your synced data (either in the android system settings > accounts or on a paired desktop at firefox > options > sync).
unfortunately i don't know of any way to totally disable top sites on the start screen of firefox on android.