This paper focuses on Byzantine attack detection for Gaussian two-way relay network. In this network, two source nodes communicate with each other with the help of an amplify-and-forward relay which may perform Byzantine attacks by forwarding altered symbols to the sources. For simple investigating the detectability of attacks conducted in Gaussian channels, we focus on the MA channel of the network, while assuming the BC channel is noiseless. Upon such model, we propose a attack detection scheme implemented in the sources. Specifically, we consider a open wireless propagation environment that allows the symbols, forwarded by the relay, to go through a continuous channel and arrive to the sources. With the observations of the source, we develop a detection scheme for the source by comparing the joint empirical distribution of its received and transmitted signals with the known channel statistics. The main contribution of this paper is to prove that if and only if the Gaussian relay network satisfies a non-manipulable channel condition, the proposed detection scheme can detect arbitrary attacks that allows the stochastic distributions of altered symbols to vary arbitrarily and depend on each other. No pre-shared secret or secret transmission is needed for the detection. Furthermore, we also prove that for the considered Gaussian two-way relay networks, the non-manipulable channel condition is always satisfied. This result indicates that arbitrary attacks conducted in MA Gaussian channels are detectable by only using observations, while providing a base for attack detection in more general Gaussian networks.