an entangling cross-resonance gate by using a microwave-only control in a tunable coupling superconducting circuit. The flux-controlled tunable coupler allows us to continuously vary adjacent qubit coupling from positive to negative values, and thus providing an extra degree of freedom to verify optimal condition for constructing the CR gate. Based on three-qubit CR Hamiltonian tomography, we systematically investigate the dependency of gate fidelities on spurious interaction components and present the first experimental approach to evaluate the perturbation impact arising from the spectator qubits. Our results reveal that the spectator qubits can lead to reductions in the CR gate fidelity relying on the particular frequency resonance poles and the induced ZZ interaction between the spectator and gate qubits, while an improvement in the gate fidelity to 98.5% can be achieved by optimally tuning the inter-qubit detuning and flux bias on the coupler. Our experiments uncover an optimal CR operation regime and provide a guiding principle to improve the CR gate fidelity by suppression of unwanted qubit interactions.