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Jesus pays the bill, even though He doesn't have too.

The temple taxes instituted in Ex 30 for the building of the tabernacle are basically voluntary, some sects pay them and others don't. They are not enforceable by law and Rabbi's and Prominent teachers are most definitely exempt.
Of course the Roman taxes were an entirely different story and everyone who's name was on the Census had to pay.

So when the guys come to collect the temple tax and they ask Peter if his master (Jesus) pays the tax, Peter automatically says, "Yes".
Jesus takes him aside and asks him if the kings of the world collect duties and taxes. The answer of course to this rhetorical question is tax and duties are levied on imported goods and the sons of the kingdom do not need to pay them.
Jesus in the same way does not need to pay the temple tax for His temple. He is the Son of God, and the temple tax is used to fix God's temple, why would the Son of the King have to pay taxes on this. It's like import duties, a nation (kingdom) charges import duties to other nations so that they may sell their stuff in the first nation. The people of the first nation do not pay the import duties, they are free or exempt.

The problem with this whole situation was:
A) If Jesus pays the tax He would be accepting the status of a regular, ordinary Jew in the eyes of the people.
B) If He doesn't pay the tax He might compromise His higher claim to being the Messiah.

So Jesus does the right thing in a gray situation. Its not black and white, there is no right or wrong answer really in this situation, its all about perception and how others would percieve the situation.

Jesus decides that as ignorant as people are of Him and His relation to the temple, and that not wanting them to stumble He will pay the taxes and Peters Share.

Miraculously too.

So what do we learn from this ??
In situations where we are conflicted and we are unsure of what to do, there is morally no right or wrong answer we can do three things A C T (adapted from Mitchell Skelton)

A --Analyze the Question
What are the positives and negatives of each answer.

C -- Consider the situation
What are the moral implications ?
Is there a commandment from God forbidding or directing our actions ?
Do we find a Biblical account (similar situation) that would bind our conduct ?
Even if Scripture does not speak directly to this situation, does it infer proper conduct for this situation ?
If you can answer no to these questions, then you are free and truly in a gray area. S what should you do.

T -- Think about the other people involved.
Even when free the believer must be prudent.
Jesus' motivation was to avoid offending the people and causing them to stumble (prov 18:19)
The Christian should always have a higher motivation in mind (that God be glorified in the situation)