I was running to work when i tried to explain you.Contestee dosnt exist, maybe that person wantes to say "conteste" and maybe with emphasis like saying "contesteeeeeee please". Conteste is of verb contestar "answer back" so... i would like to see the whole sentence but i could give you an example:
Me: Hi, how are you? Hola, ¿Cómo estás?
Me: hello??? are you there??? Hola?? estas ahí?
Me: Conteste please.
Another example:
Mario: what are you going to do today? ¿Que vas a hacer hoy?
Me: I dont know, i asked my boyfriend if he wants to go to the beach and im waiting for him to ASK ME BACK.. No se, le he preguntado a mi novio si quiere ir a la playa y estoy esperando que me CONTESTE