What does the term “implored” most closely mean as it is used in paragraph 8?

Arte you meaning this quote?

No beggars implored him to bestow a trifle, no children asked him what it was o'clock, no man or woman ever once in all his life inquired the way to such and such a place, of Scrooge.

This speaks to people in the city knowing how miserely Scrooge is. They could note beg or convince Scrooge to give anything.