I'm going to get radical and suggest that Mom can close Fingerhut if she wants to. She'd lose the benefit of a second active card. But the account, along with its six or seven pretty green check marks, will remain on her report and contribute to her overall file thickness.
As she probably knows, Fingerhut's business model is to extend credit to those whose reports are less than stellar. In exchange, customers buy cheap products for too much money. If she prefers to keep the account open for a few more months, she should follow CGID's advice and buy something. I'd spend as little as possible, then pay the balance in full as soon as the transaction posts.
For scoring, it's beneficial to report a small balance on one card, with the rest of one's cards reporting zero. Both of Mom's cards report the statement balance on or soon after the statement date. If Fingerhut has a balance of zero, this defaults to leaving the small balance on her Capital One card.
I see a couple of options for Capital One. One option is to make a small charge as CGID suggests, let the balance report, then pay the balance in full. Another would be using the card here and there, bringing the balance down to a desirable amount before the statement cuts, then paying in full once the money becomes due.
