We can shield a charge from electric fields by putting it inside a hollow conductor. Can we shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?

(N/A) No,we cannot shield a body from gravitational influence.
Gravitational force is a fundamental interaction that acts between any two masses in the universe.
Unlike electric fields,which can be shielded by placing a charge inside a conductor (where the internal field becomes zero due to charge redistribution),gravitational fields cannot be shielded.
There is no such thing as a 'gravitational insulator' or a material that can block gravitational flux.
Gravitational force depends only on the masses of the two bodies and the distance between them,as given by Newton's Law of Gravitation: $F = G \frac{m_1 m_2}{r^2}$.
Therefore,placing a body inside a hollow sphere does not eliminate the gravitational pull exerted by external matter.