We examine a distributed detection problem in a wireless sensor network, where sensor nodes collaborate to detect a Gaussian signal with an unknown change of power, i.e., a scale parameter. Due to power/bandwidth constraints, we consider the case where each sensor quantizes its observation into a binary digit. The binary data are then transmitted through error-prone wireless links to a fusion center, where a generalized likelihood ratio test (GLRT) detector is employed to perform a global decision. We study the design of a binary quantizer based on an asymptotic analysis of the GLRT. Interestingly, the quantization threshold of the quantizer is independent of the unknown scale parameter. Numerical results are included to illustrate the performance of the proposed quantizer and GLRT in binary symmetric channels (BSCs).