When you dredge up something, you bring up a topic that someone else would rather not hear or talk about. If your sister wants to annoy you, she'll dredge up that story about how you caught your dangly earring in your braces.
If your uncle loves telling stories that everyone else had forgotten about — and no one is eager to remember — your parents might say, "Let's not invite him for Thanksgiving this year. He always dredges up terrible memories!" This expression comes from the verb dredge, which means to scoop mud, trash, and other gross stuff out of a body of water.