Unhappy Impossible to reset a Gear fit

I've first connected the Gear fit to my Note and it work well but the problem began when I want to use it with my wife's S4 Activ. Even after reseting the Gear fit, it will never delete the link with the Note 3 and I'm not able to connect the Gear to the S4,
After each connection test, the gear manager is deleted from the SÁ and I must download it again to thave the same problem.
Any other way to reset the gear than the rest button at the end of the menu?
The reset button should delete the link with Note but it won't work and after restting the gear all stuff downloaded in from the note 3 is still here and ther's no connection possible with the S4 and certainly with other's devices.
Any help welcome

Thanks to have put the link to the doc on the site, unavailable on samsung sites (Gear lite not listed to)