How long does levothyroxine stay in your system?

Are the bloods being drawn to test your thyroid levels or for another purpose?

"T4 has a five to nine-day long half-life, which means that once you have become stable on it, it will take as many as nine days for 50% of the dose to clear the body.
Whether you take T4 right before your lab tests or haven’t taken it for up to 48 hours, your TSH value should be the same. Thus, you will get an accurate representation of your TSH value whether or not you take your T4 medication before a lab test.
Same goes for free T3 levels when you take a T4 medication. The free T3 level will also be relatively constant.
Levels of free T4, however, will show a peak two hours after your T4 medication is given.
So let’s say you take your T4 medication at 8 am and have your blood test at 10 am – your thyroid labs may show that your T4 is falsely elevated, and this may result in your doctor lowering your medication, when in reality, your T4 levels may be within range for the rest of the day, with the exception of that 2 hour, post dose peak.
In most cases, taking a T4 medication the morning before your lab test will not be an issue, as most doctors adjust the dosages according to the TSH, which stays stable after T4 dosing. However, to get a reading of your T4 levels that is reflective of most of the day, you would want to postpone your T4 medication until after the lab test."

What sort of blood work are you having? You will need to tell your health worker that you have taken levothyroxine. It may or may not be ok.
Levothyroxine has a half-life of roughly 7 days. This is the time it takes the body to reduce plasma levels by half. This means it will take about 4 to 5 weeks before the concentration is too low to have any effect.