I broke it, I fixed it.
I unclogged the sink, and while doing so, I sheared the meager screw that connected the strainer flange to the tail piece.
I thank the internet for answering my search of “parts of a sink” with a selection of finely rendered and labeled illustrations of sinks. That search introduced me to the term “strainer flange”.
I thank the friendly looking fellow with the contractor shirt who was browsing one bay over from me in the plumbing aisle at Lowe’s. He replied to my query, “I know you don’t worl here, but could you tell me what this is called?” By ‘this’, I mean the wet, smelly assemblage of sink parts I pulled from a Shop-Rite bag, particularly the PVC pipe attached to the strainer flange.
“Yeah, that’s a tail piece. Hmm. That one you have is some kind of novel Chinese thing. A cheap contractor part,” he said. Pointing to the metal strainer flange I had in my hand, he added, “That’s the start of what you want. You’re on the right track.”
Somewhat sheepishly, I thanked him and said I’d find a clerk to help me with the rest.
I rounded the corner and found a clerk busy with a computer. She was from electrical. “I’ll find someone to help you. I don’t want to tell you the wrong thing,” she said. As she walked away, the helpful fellow reappeared, waved a tail piece in the air, and said, “This is what you need.”
Thank you, helpful stranger!