You have to go back to the refugee camp and select the task from the chat menu to get your reward.
Viewing post in Lust Odyssey (NSFW Visual Novel) comments
I have gone to the refugee camp at many different times I have and chatted to them, it is clearly stated "Nothing here to do now".
I have repeatedly gone to the Task Menu and clicked one the Task to obtain further information and it shows that are ZERO Sand-Wyvern to been killed makes no difference.
After checking the Tasks, I yet again returned to the Refugee Camp and get the message "Nothing here to do", this I why I am certain that at some point I have claimed my reward after successfully killing the 5 Sand-Wyvern.
This Task still is NEVER moved to the completed or removed, it still permanently stuck in the Tasks we can complete.
I am 100% certain I have completed this Task and claimed my reward of 500 Experience points many, many many times and yet this Task still remains despite being completed.