I always remove those lead weights. I'm sure this is being over-cautious, but there is no harm in getting into good habits; better safe than sorry.
Lead is a heavy metal that is very toxic to all life. In the confines of an aquarium such things are riskier than they would be in the expanse of nature. Most water conditioners detoxify heavy metals should these be present in the tap water, but this detoxification with most conditioners has a limited timespan and won't continue long-term. The GH of the water also impacts the toxicity to fish of heavy metals.
I have read some very knowledgeable fish authors recommending the removal of the lead strips, and some aquarists have had fish like pleco die from presumed lead poisoning. Either way, it is not worth the risk when there are safe methods.
Byron.