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Go to that screen in VBA, load up the palette viewer, click on the first colour from that palette's row. If the value is something like 0x1234, write it down on notepad as 34 12. Repeat this for four or five of those squares along the row. Copy the string you have in Notepad and search for it in a hex editor with your ROM loaded. The offset it takes you to is the offset of the palette. Take note of the exact offset of the first value and load your ROM in APE, click "Load from offset" and enter that offset into the offset field, click search, and then edit away.