1) When the relative pronoun is the subject it is necessary in the sentence:

The dog which (that) bit the girl had rabies.

The person who killed John Kennedy has never been identified for sure.

2) When it is the object it can be omitted:

The girl whom (who, that or no pronoun at all) the rabid dog bit was lucky not to catch the disease.

3) There is a third case where the the verb "to be" is used:

The computer which was in my office has been stolen.

In cases like this it is common to eliminate the pronoun and the auxiliary verb keeping only the verb participle:

The computer in my office has been stolen.

Often it is in the passive

One of Jupiters satelites which has been photographed from space probes may be able to support life.
One of Jupiters satelites photographed from space probes may be able to support life.

The illegal immigrant who was found in the boot of Smith's car has been extradited.
The illegal immigrant found in the boot of Smith's car has been extradited.

The farm which has been identified as being at the origin of the Swine fever outbreak has been quarantined.
The farm identified as being at the origin of the Swine fever outbreak has been quarantined.

Was the ship which was lost at sea insured by Lloyds?
Was the ship lost at sea insured by Lloyds?

Note that this short cut works whatever tense of the verb is appropriate.

In this activity all you have to do is decide if the given sentence is case
A: Subject: Pronoun must be kept (e.g. The man who bought the house got a bargain.)
B: Object (Pronoun can be omitted) (e.g. The house which the man bought was undervalued)
C: Pronoun & auxiliary can be omitted (e.g The house which was sold so cheaply is going to be restored.)