The split quaternion constrained matrix equation is an important problem in mathematical research and physical applications. To overcome the difficulty in obtaining the least-squares solution of the split quaternion matrix equation, the least-squares $\eta$-Hermitian solution of the split quaternion matrix equation $AXB + CYD = E$ is considered. Firstly, anti-involution transformation and $\eta$-Hermitian matrix based on split quaternion are defined. Secondly, the Frobenius norm of a split quaternion matrix is introduced based on the complex representation of a split quaternion matrix, which dissolves the aforementioned difficulty in solving the least-squares solution. Finally, by applying the Moore-Penrose generalized inverse and Kronecker product of matrices, the least squares $\eta$-Hermitian solution and unique minimal norm solution of the split quaternion matrix equation are deduced. The feasibility of the proposed approach is verified by the numerical example.