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As stated above, :)

In theory no, in practice they do not go into the tedious job it would be to check for previous jailbreaks.

I have seen countless iPhones that have been sent to repair after a jailbreak has been removed just by a simple restore :) All passed with flying colors :)
 
In theory no, in practice they do not go into the tedious job it would be to check for previous jailbreaks.

I have seen countless iPhones that have been sent to repair after a jailbreak has been removed just by a simple restore :) All passed with flying colors :)

Restore and setup as new will erase all jailbreak traces. the phone is wipe clean and a new stock iOS is installed.
 
DFU restore and set up as new phone will leave no trace of the jailbreak, you can then sync again to get your music etc back.

DFU restore and restore from backup can in theory leave traces, as some tweaks work by modifying configuration files that are backed up. If you disable such tweaks, i.e. make your iDevice look as normal as possible before backing up, and then restore it, you will be fine. It may be theoretically possible to detect that it has been jailbroken, but it will require a significant effort, and no-one will bother.
 
DFU restore and set up as new phone will leave no trace of the jailbreak, you can then sync again to get your music etc back.

DFU restore and restore from backup can in theory leave traces, as some tweaks work by modifying configuration files that are backed up. If you disable such tweaks, i.e. make your iDevice look as normal as possible before backing up, and then restore it, you will be fine. It may be theoretically possible to detect that it has been jailbroken, but it will require a significant effort, and no-one will bother.

I am getting confused o_O, "DFU restore and set up as new phone will leave no trace of the jailbreak, you can then sync again to get your music etc back."
So is it theoretically (as stated in one of the post above) true that DFU restore + set up as new phone will not traces of jailbreak?
 
Correct, DFU-restore +setup as new will leave no traces.

If you than sync to a backup, it will reload all settings files (plist) including those of jailbreak apps.
 
If you are really worried (as in stray plist files from the jailbreak), DFU restore, do an erase all afterwards (this ensures anything stored in the data partitions is unreadable due to cryptographic keys purged), set up as a new device, then hand the device over for service.
 
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