Yes, while the idea is for the piece to be permanent, it can be easily removed by snipping the chain with a pair of snippers. If you do remove your permanent jewelry, try to snip it at the jump ring if one was used, which will look slightly different than the other links in the chain.
You can always come back to us to have inFiinite™ jewelry reattached for a small fee as long as the chain is in good condition.