The latest earnings reports from China's big four banks showed improvements across key financial metrics, but some investors remain worried that things could get worse for lenders in the world's second-largest economy.

Such concerns arose after the country's central bank, the People's Bank of China, made several moves to loosen monetary conditions as economic growth slows and as trade tensions with the U.S. worsen. That made investors fear that Chinese authorities may abandon plans to reduce harmful debt in the economy, which could hurt the banking industry.

"It may mean helping the struggling corporates ... If that's the case then we will be less optimistic about the outlook because, eventually, we will be going back to a couple of years ago when Chinese corporates struggled and relied on credit to sustain," Frank Tsui, fund manager at asset manager Value Partners, told CNBC's "Street Signs" last week.

"That will put pressure on the banks," Tsui added.

Three of the big four Chinese banks saw their shares in Hong Kong fall last week. Industrial and Commercial Bank of China tumbled 0.87 percent, China Construction Bank declined 0.58 percent and Bank of China was down 0.28 percent. Agricultural Bank of China bucked the trend with a 2.15 percent climb on stronger earnings.

Their Shanghai-listed shares fared better. CCB was up 1.28 percent over the week, and ABC and BOC both inched up around 0.6 percent. ICBC was the only big four bank that ended the week in the red on the mainland after declining 0.91 percent.