In sub-carrier modulation (SCM) wake-up radio (WuR) enabled wireless sensor networks, a node can initiate data transmission at any instant of time. In this letter, we propose to activate a backoff procedure before sending wake-up calls (WuCs) in order to avoid potential collisions among WuCs. Consequently, no backoff is needed for the main radio after a WuC is received. A discrete-time Markov chain model is developed to evaluate the performance. Numerical results on network throughput, energy efficiency, average delay, and collision probability reveal the benefits of enabling backoff for SCM-WuRs, especially under heavy traffic loads or saturated traffic conditions.