I dont think it hurts them but also maybe not a good idea. Look at #9 here... http://www.turntechbattery.com/TurnTech Battery/FAQ.html
I have a Moty Design for my 08 610 which I've had for a year and really like. Same chemistry.....Iron Phosphate........and most of these designers recommend not using a tender......for some reason. The battery does keep a self life charge for very long periods.
All lithium iron batteries require a battery management system. This system must be either in the charger or the battery itself. Our Earthx batteries have this battery management system built into the battery so that a regular charger can be utilized.
I have the turntech in my 570 berg and I have a Moty in the TE 610. I was told not to use a tender on the Moty. But you're saying they are the same and it's ok to use a tender on the TT battery? I don't understand how it's ok for one and not the other?