By George Georgiopoulos and Balazs Koranyi ATHENS/FRANKFURT (Reuters) - Deposits are trickling back into Greece's banks, banking sources said, offering some practical justification for a mainly symbolic move by Athens to cut the system's reliance on emergency central bank funding. Closed for much of July, Greek banks have been kept on a funding drip by the European Central Bank for most of this year and Athens, which is on the verge of clinching an 86 billion euro (60.6 billion pounds) international bailout, is still limiting cash withdrawals to prevent a run on deposits. Hoping to shore up confidence in the lenders, Greece asked the ECB late on Tuesday to cut its Emergency Liquidity Assistance (ELA) to 89.7 billion euros from around 91 billion, arguing that the system had amassed a big enough buffer as confidence returns following the bailout agreement.