Based on this discussion, I see there is no real way to delete old backtests.  The solution today is to clone your project delete the old one that has all of your backtests.

While running the API Unit Test cases in Lean, I found this.

 // Delete the backtest we just created
var deleteBacktest = _api.DeleteBacktest(project.Projects.First().ProjectId, backtest.BacktestId);

Unfortunately the assertion fails with the response that it cannot find the projectId.  

{"errors":["Project not found."],"success":false}

I believe this is a bug that the guys have just not gotten to.  Propably the reason you can't use the qcli to delete a backtest either.

Can anyone confirm this?