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

It means like answer me please... if you ask someone "how old are you?" and that person dosnt ask you back you can tell that person "conteste" i would say "contesta" though