The rapid test that you used is not as specific or sensitive as the Gas Chromotography or Mass Spectrophotometry systems that they will use in the lab.
These instruments can easily run $100Ks+ each and can detect drugs of abuse at levels as low as 1 part per billion.

Luckily, labs will give you a cut-off level to ensure that a "positive" is truly a positive with the benefit of the doubt on your side.

I would stay clean and dilute yourself just before going in anyways. You want your piss to look as clear as water.
If you have to go in a 2nd time then you will do so several days later.

Everyone's metabolism and retention levels are going to differ. I would guess that 80% of the folks that smoke 1/4 per month will be clean after 2 weeks of quitting.

However, you should always go in well prepared.