It would seem to me that one would use a discount rate that is reflective of the risk of the asset--which in this case would be the opposite side (bid or ask depending on whether you are reverse repo or repo) of the repo rate for the remaining term of the repo agreement.
Given the short term nature of these trades, these are generally held to maturity of the repo agreement and consequently not much attention is made to the mark to market. Of course the minute one puts the trade on, they will be underwater by at least the bid-ask spread but as they are held to maturity and short term in nature, they will be rarely liquidated. Unless the collateral is "special", there will generally be substitutability of the collateral and will generally only be liquidated if the collateral is sold or the trade needs to be unwound for liquidity or cash flow reasons.