You could always opt for a more powerful router...and stop the rental fees. Yes?
WiFi extenders are not compatible with modems or an eMTA. Extenders are only compatible with routers. You may have an all-in-one device (Internet, telephone, router), but WiFi extenders will only communicate with the radio antennae on the router side of the device. WiFi has nothing to do with DOCSIS or telephony.
As long as the extenders operate on the same WiFi standard as your router, it'll work. The standards are 802.11a, b, g, n, ac and eventually ad. Your Technicolor CGM4141 is compatible and backward-compatible with all those standards.
It's not a question of WiFi extenders being compatible with specific devices. If an extender is certified WiFi, it'll work with any other WiFi device because it complies with an IEEE 802.11 protocol (a-ad).
Your greatest concerns for extenders are power, features and setup. You should search WiFi extender review 2019 to find expert recommendation. Read a few reviews and user comments before you buy.