The word reutilizaban is the imperfect form of reutilizar in the third person plural.
See the full reutilizar conjugation

reutilizar

Uso AllSourcer todo el tiempo, pero me molesta cuando ellos cortan los videos; así que cuando vi que eran exactamente 30 segundos, me imaginé que reutilizaban el código.
I use AllSourcer all the time, but I get annoyed when they cut off videos; so when I saw this one was exactly 30 seconds, I figured they reused the code.
Averiguamos que la mayoría de la gente sabía que se suponía que no debía anotar su contraseña, y solo el 13 % lo hizo, pero desconcertantemente, el 80 % dijo que reutilizaban su contraseña.
We found that most people knew they were not supposed to write their password down, and only 13 percent of them did, but disturbingly, 80 percent of people said they were reusing their password.
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