Banks had paid $21 billion through this past summer to repurchase souring home loans from Fannie Mae and Freddie Mac, the taxpayer-backed mortgage companies, under contracts that oblige lenders or loan servicers to buy back loans that aren’t up to snuff.

That covers about 13% of the mortgage companies’ credit losses since their government takeover, according to a report released this month by the Financial Crisis Inquiry Commission (see pages 224-225).

Yet it’s just a sliver of the $529 billion of profits U.S. banks booked during the heyday of the housing bubble, between 2003 and 2006 — and it may be just a small fraction of the sums they will fork over in looming mortgage battles with insurers and private investors.

Estimates of bank exposure to so-called private label mortgage putbacks run into the tens of billions. Settling remaining claims by Fannie and Freddie, by contrast, may not cost much more than a few billion — which makes it that much more exasperating to see the banks playing their foot-dragging games.

The bank that has gotten the most bad mortgages bounced back to it by Fannie and Freddie is, no surprise, Bank of America (BAC), the North Carolina-based owner of the notorious Countrywide subprime mill. Over the past four years, it got $6.9 billion in repurchase requests from Fannie alone – as much as its next four competitors combined.

Data released by the FCIC show the bank paid Fannie and Freddie almost $6 billion over the past four years to settle mortgage repurchase requests (see chart, right) – and that was before the settlement this month under which it forked over an added $2.8 billion.

Yet despite that show of comity, the banks aren’t going quietly. For every three bad loans repurchased as of September, there were two more requests from Fannie and Freddie that the banks hadn’t honored.

That number has come down some since Bank of America and Ally, formerly known as GMAC, agreed to settlements with Fannie and Freddie. Even so, some $10 billion of repurchase requests remain open – and there is some evidence the banks have been dragging their feet in paying up.

As of September, about a third of the outstanding repurchase requests issued by Fannie and Freddie had been outstanding for at least four months, the companies said in their latest quarterly filings with regulators. Banks, “including many of our larger seller/servicers, have not fully performed their repurchase obligations in a timely manner,” Freddie noted in its filing.

The firm went on to say the banks’ tardiness had caused it to “begun to require certain of our larger seller/servicers to commit to plans for completing repurchases, with financial consequences or with stated remedies for non-compliance, as part of the annual renewals of our contracts with them.”

The struggles of Fannie and Freddie to collect on their repurchase demands are remarkable because rules are on the government-sponsored entities’ side. The contracts they sign with mortgage originators and servicers give Fannie and Freddie the clear right to force bankers to buy back loans that fail to meet the companies’ guidelines.

By contrast, the rules in private label disputes – ones pitting the banks with investors such as pension funds that bought mortgage-backed bonds without Fannie and Freddie’s involvement – are much murkier, a situation the banks expect to use to their advantage.

Even so, analysts at Deutsche Bank, for instance, expect Bank of America to shell out $15 billion or so to settle private label mortgage disputes in coming years — well above the $9 billion analysts expect it to pay to settle its Fannie-Freddie liabilities. That’s because the underwriting on the private label bonds tends to have been so much worse, which has translated into many more suspicious-looking early defaults to make good on.

In contrast, the numbers presented in the FCIC report make most of the big banks’ exposure to Fannie Mae mortgage repurchases look downright manageable. Were they to settle on the same terms as BofA, for instance, Wells Fargo (WFC) would pay Fannie $321 million, Citi (C) $247 million and JPMorgan Chase (JPM) $193 million. Unlike Fannie, Freddie Mac didn’t disclose outstanding repurchase requests by bank in its FCIC submissions.

But now that the worst actor, Countrywide, has cleared up many of its disputes with the GSEs, the stakes are apparently so low that no one is in a hurry to settle.

“It’s kind of the moot point, but if [Fannie and Freddie] wanted to settle it all at once, it’d be fine with us,” JPMorgan Chase chief Jamie Dimon said this month on the bank’s conference call.