Any ungrounded metal thing between the charged source and the ball will tend to become charged and then become a source that would tend to charge the ball. A grounded thing would share the charge it receives with the earth and mostly prevent the ball from being charged. It would most effective at preventing the ball from being charged if it is larger than both the source and the ball. The most effective aspect of the size would be the area, thus a large flat thing would be more effective as a shield than a ball that is not so large.
Electrostatic induction by itself does not charge a nearby object. A charged object that is brought near another object only attracts or repels electrons or positive ions that can move in that object. If a conductor is connected to a more distant point on the second object the electrons can be repelled through that conductor to a third object or to earth. If the conductor is then disconnected, the second object is then left with a deficit of electrons and a positive charge.
Shielding an object from any influence of a nearby charged object can be accomplished by providing something between the object and the charged object that can effectively redirect that influence by providing a place for charge redistribution that allows electrons to flow to a place like the earth that can absorb an "infinite" number of electrons without much charge imbalance.
