The British Empire ran into a ton of debt after the Seven Years' War (about 130 million pounds, which was the most any country has ever been in debt for up to that time in history) and one of the ways to pay back some of the debt, the Parliament decided, was by fully enforcing taxes the Americans were allowed to not pay during the time of Salutary Neglect and by establishing new taxes as well.

I've written about the strain that these new taxes created between the American colonists and the British Parliament before, so I'll just leave the link here or read a more detailed description in the source I've left below.

What's really interesting about the Tea Tax is that it was meant to be a compromise at first. The Townshend duties were established by the British Parliament in 1767, taxing the American colonies on several goods like paper, lead, glass, and tea. By 1770 these were so unpopular in the colonies that all of them had been repealed, except for the tax on tea. That compromise calmed tensions down for a few years.

But then came the British East India Company and the Tea Act in 1773. The British Parliament basically gave the East India Co. a monopoly over the American market in order to provide it with revenue (the Company was in deep financial trouble at this point). Now, the tea that it supplied would stay as the cheapest tea on the market, so it's not like the British were increasing prices at the same time they were granting the monopoly. But, the colonists were used to Dutch tea and were not happy about the monopoly that the Company received. The Sons of Liberty and their radical supporters became afraid of future taxes and a slippery slope, thinking that maybe for now it's only a monopoly on tea, but in the future the British could establish a monopoly on any good they wanted based on the principle of the Tea Act. In order to make sure that the rest of the colonists were not tempted by the idea of cheap British tea, they decided that the East India Company tea could not touch American shores—ensuring the Boston Tea Party in December of 1773 and other similar confrontations throughout the colonies.

But that also doesn't mean that the British just wanted to act tyrannically towards the colonists. Many of the taxes that the colonists were refusing to pay have long been collected in Britain already. And the Seven Years' War was partially fought on the North American continent, so the colonies relied on the British military during the war. The mood in Britain was that the Americans were ungrateful for the protection that the British offered to them and were refusing to pay their taxes as British citizens.

Given that the Parliament was in charge of collecting taxes in Britain, it could not simply give in to the colonists from a political standpoint. Reversing all taxation on the American colonies would be equivalent to giving up the idea that the Parliament could rule over some of its people and giving up the idea that the Parliament was superior to colonial legislatures. If the colonists could refuse to pay taxes imposed on them, couldn't they just refuse to follow any law established by Parliament? What if the merchants in England would start to copy that tactic and begin to hold the Parliament hostage when it came to their taxes? What if everyone in England just began to refuse to pay taxes, saying that if the Americans could, why couldn't they?

So, in short, that's why the British kept the tea tax as a more or less symbolic tax on the American colonists and how that has led to the Boston Tea Party.

Source:

http://www.taxhistory.org/www/website.nsf/Web/THM1756?OpenDocument#1756