Is it wrong to re-introduce an animal to a place where it has already went extinct?

[Young Patriot]

The giant ditch frog or "mountain" chicken - Leptodactylus fallax went extinct on my island a couple of decades ago. It went extinct due to a number of reason, mostly the introduction of the indian mongoose, but measures are being placed to eradicate or at least lower the numbers of mongoose on the island. If we are successful in eradicating the mongoose, do you think it will be safe to re-introduce the frog?

More info on the frog:

Leptodactylus fallax, commonly known as the Giant Ditch Frog, is a species of frog that is native to the Caribbean islands of Dominica and Montserrat. The population has declined 80% in the last ten years and this species is now critically endangered. The population is estimated to 8000 individuals. One of the main threats is human consumption. The fungal disease chytridiomycosis has also had a dramatic effect on the population. Locally, it is known as the Mountain Chicken for its large size and the fact it is hunted for food. As of 2007 on the island of Montserrat, if not before, eating the mountain chicken is discouraged because of its decreasing population.

The Giant Ditch Frog is terrestrial and nocturnal. The adults are 16 cm (6.3 in) long.

The frog was formerly found on the islands of Guadeloupe, Martinique, Saint Lucia and Saint Kitts and Nevis. In February 2010, volcanic activity from Soufrière Hills on Montserrat resulted in ash covering large parts of the frog's habitat on that island, further endangering the species.