Because you have already accounted for the GST and you will your GST as a reduction to the GST from Sales you send to the government you can charge them just for the amounts without the GST. 

How have I already accounted for the GST? 
I am not charging anyone. The employee paid their phone bill with their own money. I want to reimburse them as a vendor and pay them what they paid. But when I record, I'm wondering if I record the GST paid when posting as if it were a regular invoice. 

Maybe I misunderstood your question.  So it was the employee who paid the bill that had the GST on it and you want to know when you pay him back do you included GST when you reimburse him?  If so then yes you can record GST when you refund him. 

Perfect yes that's exactly what I needed to know. Thank you.

Hi Terrace Steel Works Ltd , if this suggested answer helped, please mark it as verified  (by clicking the "…" button next to Reply, on the response) for the benefit of others in this forum . Thank you!

Hi Terrace Steel Works Ltd , if this suggested answer helped, please mark it as verified  (by clicking the "…" button next to Reply, on the response) for the benefit of others in this forum . Thank you!