。
I imagine you didn't even have time to write a reply.
Literal
Reply [object-を] write free-time [even-も] didn't-have [probably-のだろう] [quotative-と] humbly-surmise.
A keigo showcase. お察しいたします layers the humble お + stem + いたす (the most deferential form of する) onto 察する (to surmise/sympathize). The だろう softens the assumption, and と quotes the whole supposition. This is classic business courtesy — delicately acknowledging someone's busy schedule rather than pressing for a reply.