Re: folder reappearing on desktop

You presumably have a Sync (or Custom) profile that is set to replicate files that are on one side only to the other.

In the Free versions, you can only set such two-way Sync to replicate 'absence' or 'presence' (delete the one-side-only file, or copy it to the other - but not both, because how would it know which action to take?). Thus, it re-copies it back from the Destination/Right (until you move the Destination copy) - because you have told it to.

Help > Search > 'basic synchronization' (without the quotes) > top two hits

for what can be done (or not) in the various versions