I think that what you have is a basic Survival Analysis problem. (According to Wikipedia, This topic is called reliability theory or reliability analysis in engineering, and duration analysis or duration modeling in economics or event history analysis in sociology).
Your response variable seems to be time to event with censoring to the right, that is, there are some homecomings you don't register because your experiment finishes before (or maybe because they never happen). What you can obtain with this analysis is the probability of being recaptured given time from release and any other covariates.
You can try with library survival in R, if that's your software of choice. Many other softwares have equivalent tools to work with this kind of data.