what does "a pair of sow's ear"mean?
“No, well, he’s not usually shy about them. It made an extra bond between Lula and me, the fact that Uncle Tony considered us a pair of sow’s ears. It was worse for Lula; at least my biological parents must have been white. Tony’s not what you’d call unprejudiced. We had a Pakistani trainee last year; she was one of the best we’ve ever had, but Tony drove her out.”

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There's a saying, "You can't make a silk purse out of a sow's ear." It means if you start with poor quality materials, you can't make something nice. The person speaking and Lula were both adopted and Tony apparently considered them "poor quality material", perhaps because of race, in Lula's case.  In Tony's opinion, even though they were raised by presumably good quality people, they couldn't hope to overcome their inferior beginnings.

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it means a great couple who love making mess and never felt shy to do that.