The 시 in the 주셔서 is an honorific infix added for politeness, status, etc.
Without the 시 it would be 읽어줘서 감사해.
To break it down even further:
Verb + 아/어 주다 (providing a service) + 시 (honorific) + 아/어 서 (sentence conjunction)
읽어주셔서 감사합니다 = Thank you for reading (when talking to a teacher or older adult, for example).