I am not sure exactly why your colleague suggested you ignore the FX delta risk for the repo but as @kurtosis suggested, perhaps the loan (ultimately repo is collateralized lending) is in the same currency as the collateral. Or perhaps there is an FX forward that your firm has on to hedge the FX risk for the term of the repo.
Technically, there is nothing to prohibit the possibility of FX risk to be in a repo trade. For example, if you are the lender and buy the collateral from the borrower, and the collateral is denominated in a different currency than your functional currency (ie sovereign local currency bonds), you will be exposed to FX risk. You will be required to sell the collateral back to the borrower at the contracted local currency price and will then be required to convert the local currency proceeds back to your functional currency.
If your firm has local currency needs and maintains a balance of local currency to serve cash flow needs in that local currency, they may be unconcerned about the FX risk. Alternatively, there may be an offsetting hedge through a FX forward that has locked in the rate at which they will be converting the proceeds from the collateral sale back to your firm's functional currency--thereby eliminating any FX risk.