If it's in warranty - contact support. I'm not aware that Fitbit have a return policy so the correct recycling of the device falls in their court. The mods may provide more info on any recycling programme?
We have to be the ones responsible for correct disposal - which means a lot of owners will simply turf these devices in the rubbish bin! Out of sight, out of mind kind of thing.
These devices are not repaired or repairable - other than band replacement. They would have to be sent back to China for repair. Not worth it for a cheap mass produced device. The cost of development was paid for a long time ago. Now they are churned out for a cheap price, and there is no incentive for repair. Actually if you look at the device - it's not designed to be serviced. It can't be successfully opened like a watch.
If the charging port has "melted", that suggests either a charger fault - although the charger should have failed quickly preventing heat damage to the device - OR a fault with the device.
If the device is out of warranty, then I suggest you try and have it disposed of through an electronics recycling programme. I'd hate to think how many of these devices make it to landfill, instead of appropriately being recycled. There must be small amounts of nasty stuff inside, as for all electronics, apart from general plastic pollution.
