Let me give the following verse that I had read several years ago. It may explain how the word हेतु is used.
Before we go to the verse, some explanation of its background will be helpful.
In old India, when the caste feelings were quite strong, two castes, the Brahmin and the Kayastha, were always opposed to each other, mainly because both castes derived their livelihood from being literate, the Brahmin as a priest/clerk/astrologer and the Kayastha as the village clerk. The Brahmin abstained from meat eating while the Kayastha had no such compunctions. The Brahmin and the Kayastha would use every opportunity to jeer at the other.
A Brahmin wit has composed the following verse. It involves a pun on the meaning of कायस्थ - it can mean someone of the कायस्थ caste or it can also mean the literal 'one who is inside a काया or a body', i.e. a child in the womb.
The verse says:
कायस्थेनोदरस्थेन मातुर्मांसं न भक्षितम्।
न तत्र करुणा हेतुस्तत्र हेतुरदन्तता॥
A कायस्थ in the womb did not eat the mother's flesh. It was not for the reason that he took pity on her. It was for the reason that he had no teeth!
Arvind Kolhatkar, Toronto, November 21, 2013.