If banks feel pressure to return the money just to avoid compensation restrictions or to appear strong, that could prove detrimental for both the banks themselves and the country's economic recovery effort.
Currently, institutions that want to repay the government must notify the Treasury Department and the appropriate federal banking agency about their intentions.
"After receiving your notice, Treasury and your primary regulator will consult about the request," the Treasury Department says on its Web site. "When all consultations have been completed, we will contact you to discuss the redemption request."
Analysts caution that Goldman Sachs, unlike some other big banks, is not a consumer-based lending bank and therefore is in a unique position to return its TARP money.
"They can easily raise money in the markets," Egan noted.
This difference is one reason why Scott Talbott, senior vice president of government affairs at the Financial Services Roundtable, believes that institutions will not feel pressure to return any aid they have received.
"Many banks will choose to remain in TARP," he said, adding that "each bank makes its own decision about TARP."
The real risk that banks face, he said, is not returning government money for the wrong reasons, but rather the risk that "the government will change the rules after the fact -- that is a real risk."
All in all, Talbott said, it is a good sign that banks are returning the money.
"It shows signs of strength that Goldman is able to raise the capital to help repay the TARP funds," he said. "There is liquidity in the markets and confidence in the markets and the industry is returning. Stock prices are returning to normal. This benefits investors, 401k plans, and the economy."