Was the 2-drachma tax collected for the temple in Mat 17:24?

[tonychanyt]

English Standard Version, Matthew 17:

24 When they came to Capernaum, the collectors of the two-drachma tax went up to Peter and said, “Does your teacher not pay the tax?”

New International Version:

After Jesus and his disciples arrived in Capernaum, the collectors of the two-drachma temple tax came to Peter and asked, "Doesn't your teacher pay the temple tax?"

The word "temple" is not in the original manuscript. Is NIV justified to add the word "temple" in its translation? Was the 2-drachma tax collected for the temple in Mat 17:24?

Yes, it originated in Exodus 30:

13 Each one who is numbered in the census shall give this: half a shekel according to the shekel of the sanctuary (the shekel is twenty gerahs), half a shekel as an offering to the LORD.

Ellicott explained:

It was fixed at a half-shekel a head, and the shekel being reckoned as equal to four Attic drachmæ, was known technically as the didrachma (Jos. Ant. iii. 8, § 2).

half a shekel = 2 drachma

It was collected even from the Jews in foreign countries, was paid into the Corban, or treasury of the Temple, and was used to defray the expenses of its services. After the destruction of Jerusalem, Vespasian ordered that it should still be collected as before, and, as if adding insult to injury, be paid to the fund for rebuilding the Temple of the Capitoline Jupiter (Jos. Wars, vii. 6, § 6).