My grandpa taught me how to do this along time ago and I figured because this is the site that is the depository for all how toing knowledge why not add my own weird trick.
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Step 1: Locating the Strip
Take American paper currency more than the one (one dollar bills do not contain the magnetic strip) and hold it up to a bright light. I recommend doing this with five because this may make it so that you can't use the bill in a vending machine or at least it will think its a one. I also recommend that you do this with an old bill because it makes extraction easier. When you look through the five you should see a strip of something that has the words USA FIVE written in small black print on it.
Disclaimer: This may be illegal. This is only for informational purposes.
Step 2: Preparing for Extraction
Now that you know where the strip is you have to loosen it within the two layers. I do this by folding the bill along the strip. Then hold the fold in between your thumb and pointer finder and role the fold back and forth. If you do this with a new bill you should see a kind of pocket in the shape of the strip forming. You want to do this thoroughly along the whole strip to make sure its completely loose.
The below picture is a side view of the five.
Step 3: Extraction
Now that the strip is completely loose go to the top of the bill and make a very small tear as close to being on top of the strip as possible. The tear should just come to the top of the black line. If the tear was in the proper spot you should be able to work the two layers apart and see the end of the magnetic strip. Now grab the end of the strip and pull it out. If your loosening was done well it should slide right out. You may want to use a forceps for this but it's your choice.
I'm not sure if this is legal. I think it may fall under the defacing of money.
It might also make a vending machine think your fives a one I haven't tried it yet but i think that's how a vending mahcine knows when you give it different bill types.