It takes a moment for things to connect in his head. Inigo has to think about it, but through her wording he manages to realise what's going on here. I saw into his heart, if only briefly, as he saw into mine.

Inigo thinks back to the island. To the talk he had with Gerome, that night when they had been lying together under the stars. When Inigo had confessed to Gerome about the vision he had seen, and Gerome had said.. What was it? I believe the vision, the memory, was a woman's.

Then this must be said woman, right? The person Gerome shared memories with, just as Inigo had with Gyousou.

"Ah.. I see." It's all Inigo manages to force out before he's overwhelmed by yet another force of tears, brought on by Zelda's other words, those last ones. He covers his mouth, sniffs, and then shakes his head. "F-Forgive me, milady, I know this isn't a state to be seen in.." And yet he can't help it. Now the dam of the tears has burst, there's no stopping them anymore.

"I mean, I just.. I just cared for him a lot."

As did Gerome about him. It was something Inigo figured through the things the other said, no matter how subtle at times, but it's something else entirely to have that confirmed so directly by a third party.