The real reason for their backdown is that Hong Kong Human Rights and Democracy Act in US will be likely to pass. This bill will punish HK official for violating human right. And potentially forbidden the use of financial services like Visa and Mastercard.

However, it's not even a real backdown though. She just announce to start a motion to backdown, but it was still the decision of parliament to withdraw the bill, and the parliament was controlled by pro-Beijing parties. Practically even pro-Beijing parties care the voter's view so it may withdraw the bill, but it was uncertain whether there were an order from Beijing to vote down withdrawal after the protest was over, so still many uncertainty right here. Not to mention police brutality was not addressed.