You're mixing up your Reagan-era Iran scandals.

First, there was the Iran Hostage Crisis, where Iranians stormed the US embassy and took a bunch of hostages in 1979. While I have no doubt there was Republican fuckery going on, Carter really didn't do himself any favors with his handling of that. The hostages were finally released, after more than a year, the day Reagan was inaugurated

https://en.m.wikipedia.org/wiki/Iran_hostage_crisis

Iran-Contra was a scandal where the Reagan administration sold arms to Iran (who was fighting Iraq, then an American ally), circumventing Congress. They then gave the money to the Contras, a group of rebels in Nicaragua, again circumventing Congress:

https://en.m.wikipedia.org/wiki/Iran%E2%80%93Contra_affair

You are correct that part of the goal was to release hostages, but those hostages were taken by the Lebanese well after Reagan's first election.