They talk.
Given that SCP-682 has spoken coherently, even eloquently, during multiple termination attempts, the Foundation can in principle form a psychological profile of it just as they would on a hostile humanoid. What she decides to argue is that the Foundation is remiss in not having done so already; even in cases of intractably hostile humanoid anomalies, there's precedent for psychological profiles like these facilitating less expensive and more effective containment, cf. 353, 076-2, et cetera, and there's no reason a priori to treat SCP-682 differently just because it's not human-shaped. It's already communicated more intelligibly than some humanoid anomalies that have successfully been psychologically profiled.
A great deal of the work of profiling SCP-682, she believes, can be done simply by going over the records of its previous communications and actions with an eye toward modeling it as though it were a human being that's monster-shaped, rather than (as the Foundation seems to have been modeling it so far) a dangerous animal that happens to be able to talk. In principle there's no need for Charlotte to talk to it at all. But the elephant in the room is that, now that SCP-053 is an adult, there's an enormous opportunity to learn more about SCP-682, sitting there waiting for the Overseer council to grab it, and the longer they leave this particular twenty dollar bill lying on the ground the more money they spend on constantly replenishing 682's acid bath. And with Dr. Leonard Salt and O5-1 herself as DELTA/AGENT designees, risking a containment breach is less costly in personnel and human lives than it was decades ago when SCP-682 was initially contained.