(1) Why was it important that Andrew rub the robot with grease?
(2) Why was it important that Andrew rubbed the robot with grease?
In the first example, the word rub is in the plain form. This particular case is an example of what some writers call the subjunctive; it isn't the present simple of the verb rub. We can see this because there is no third person suffix, 's', on the end of the word. The example does not say:
- Why was it important that Andrew rubs the robot with grease?
We see the subjunctive in content clauses after certain verbs and adjectives. So for example we might see:
- It is important that he be there on time.
- They suggested she take the other exam.
If the sentences above used the present simple instead of the plain form, we would see the forms is and takes instead of be and take.
Meaning
Sentence (1) presents the situation as being important before he actually rubbed the robot. As the Original Poster hints, it isn't necessarily the case that any rubbing of the robot did actually take place.
Sentence (2) is ambiguous. It could mean the same thing, or it could mean that after he rubbed the robot, the fact that he had rubbed it was significant or important in some way. This reading isn't available from sentence (1).