This very websites opinion -
"Is it possible to inject insulin through clothing?
There are several reasons why injecting insulin through clothing is a bad idea, however convenient it may seem. Both syringes and pens are lubricated in order to make them as painless as possible. Clothing can remove this lubrication, meaning injections can be more painful.
Clothing is not sterile, and substances on the clothing may contaminate the needle and at its worst this can lead to infection. Furthermore, clothing can damage the effectiveness of the needle by dulling the tip.
Possibly most seriously, clothing restricts your view of the injection site, leaving the patient unaware of the effectiveness of their injection. "
Edit, I've been trying to think of a witty analogy for this, but the closest I'm getting is thinking about emptying a paper punch and removing the punched holes....