Due to the open accessibility of wireless networks with severe privacy risks, covert communication has gained increasing attention, where the effective range is limited by the low transmit power. Fortunately, employing intelligent reflecting surface (IRS) as a relay has become an appealing solution to extend the range of covert communication. To this end, we investigate the covert communication in which the ground transmitter secretly delivers information to the full-duplex receiver through a two-way IRS, avoiding detection by the warden. Then, the error detection probability is determined with an optimal threshold at a warden, which is the worst case for covert transmission. Moreover, we analyze the closed-form expression of outage probability. To improve the covertness, artificial noise is generated by the receiver to interfere with the adversarial monitoring. Thus, considering the optimal prior probability, we maximize the expected error detection probability of warden subject to the covertness constraint. Specifically, we alternately optimize the prior probability and the transmit power of artificial noise while satisfying the outage probability and covertness requirement. Numerical results demonstrate the effectiveness of the proposed scheme for covert communications via the two-way IRS.