Is the Hadith that mentions a thousand good deeds for killing a gecko with one strike, five hundred good deeds for two strikes, and a hundred good deeds for three strikes authentic or weak, and what is the wisdom behind killing this specific type [of creature]?

It was narrated in Sahih Muslim, Sunan Abi Dawud, and Jami' al-Tirmidhi, from Abu Hurayrah (may Allah be pleased with him), that the Prophet (peace and blessings be upon him) said: "Whoever kills a gecko with the first strike, one hundred good deeds will be recorded for him. For the second strike, less than that, and for the third, less than that." It was also narrated in Al-Mu'jam Al-Awsat by Al-Tabarani, from Aishah (may Allah be pleased with her), that the Prophet (peace and blessings be upon him) said: "Whoever kills a gecko, Allah will erase seven sins from him."

Imam Al-Nawawi mentioned that the restriction of good deeds to one hundred or seventy can be understood in several ways, including that the concept of the number is not to be acted upon, or that the increase was a charity from Allah, or that it differs according to the intentions and sincerity of those who kill them.