Reimbursement from family for a Credit Card purchase

There are two possibilities:

1. Add an Offline Checking account to your Quicken data file, e.g., "Billy owes me", Opening Balance 0.00
   Record the credit card (or cash) purchase as a transfer to the "[Billy owes me]" account
   When Billy pays you back and the e-transfer appears in your checking account, record that again as a transfer to "[Billy owes me]". This should reduce the outstanding balance.
   You can see at a glance, by looking at the Account Sidebar or the account register, how much money Billy owes you
2. Create an Expense Category "Billy owes me"
   Record the purchase to the "Billy owes me" category
   When Billy pays you back, again record it to the "Billy owes me" category
   Look at the Budget view to see how much Billy owes you. Or create a report, Easy Answer, How much did I spend on … selecting the "Billy owes me" category, to see Transaction Detail

I assume you have decided to go with option 2.

When the e-transfer appears in your checking account … yes, change the category to the "Billy owes me" category. This will reduce the amount outstanding. Looking at the category, you will be able to see how much Billy still owes you.