According to the easy-to-find label on the Telo power supply, the Telo takes 5 volts DC. Let's take a little time to examine your intention. As a point of departure, let us seek to maximize efficiency when mains power is active. The time spent running on the UPS, with mains power failed, is negligible; so we won't worry about efficiency in that condition.
Option 1: the way normal people (or engineers like me) would do it. Small UPS providing AC, with the Telo and modem power supplies (wall warts) plugged into it. When mains power is active, the total load consists of: (1) the Telo, which is running from the mains because the UPS has connected it to the mains; (2) the modem, similarly running from the mains; and (3) a very small load from the battery charger in the UPS. Since the Telo's wall wart is optimized for 5vdc out, it's about as efficient as it can be; similarly the modem's power supply is optimized for the modem.
Option 2: supplying DC for the Telo and for the modem from the UPS, which implies they're running from the (probably 12v) storage cells in the UPS. The charger in the UPS has to be a little larger because it is now not just floating the batteries but also supplying the Telo and the modem. The battery voltage (probably 13.5v float voltage) now has to be regulated down to 5v for the Telo, and whatever the modem requires also. There's an additional regulator in there, with associated energy loss. Depending upon the level of sophistication of the regulators, you're wasting between about 5% and about 63% of the energy taken from the batteries. Not smart.
Remember that the Telo's own supplied wall wart is, with overwhelming probability, more efficient at providing 2a at 5vdc than a regulator on a 12v battery could possibly be. The same is also true for the modem's wall wart.
Too, with option 1, you can run other things from the UPS. Your PC, for example, and a router. Besides wasting less energy, it's also cheaper (likely MUCH cheaper) to purchase, and more reliable, because failure of the UPS doesn't kill your phones and other stuff as long as mains power is on -- while with option 2 a UPS failure is added to the list of things that kill your phones, even with mains power available.