The implied interest rate based on Treasury bond carry arbitrage will decrease when the cheapest-to-deliver bond price increases,everything else held constant.

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In Treasury bond carry arbitrage, an investor buys a lower yielding Treasury bond and sells a higher yielding Treasury bond to earn the carry (the difference between the two yields). The investor shorts the higher yielding bond by selling it and delivers the lower yielding bond at maturity. The cheapest-to-deliver bond is the bond with the lowest cost for the investor to deliver at maturity. If the price of the cheapest-to-deliver bond increases, the cost for the investor to deliver that bond decreases, making the carry more valuable. Therefore, the implied interest rate based on Treasury bond carry arbitrage will decrease.

The Implied Interest Rate Based on Treasury Bond Carry Arbitrage