Marking up or not marking up doesn't change the reality. What you buy is Expense, or Cost of Goods Sold (for products you bought to sell, such as inventory). What you "get reimbursed" simply is the Sales Price, as revenue or income. Your reporting shows the difference = the Net Income, which is part of taxes. Examples:

I buy $100 of Stamps to use for your project, and I charge you $100 for that cost, at Cost. That means I have $100 gross Postage expense and $100 Gross Sales Revenue and I net $0 for Profit, and if that sale item is subject to sales taxes, I was supposed to assess you for that, as well.

Reimbursement is a Process, not the Expense Account reason. Reimbursement related to customer activities is Sales, not washing away your expense.

Yes, if you get a prepayment, and are a Cash Basis Entity, you just got Income. That is what the IRS considers it when someone gives you Funds.

Don't examine Banking. You examine the reasons the funds move. You would not post your purchases as negative income; they are your expenditure. They are not the Income event, but the expense event.

Do this Right; not with some imagined offset method. Meet with your own CPA to learn how to manage Gross, see Net, and manage Banking events.