if you remove the protection, then it wont have the protection anymore :-( and the protection is a good reason to use a pre-assembled battery unit like that.
the other 2 connections can be the "DATA" that can be used by a more computerised device to determine the actual usage, and its capacity from that actual usage, and or a thermister, for the charging, to insure that the cell is not in heat danger when charging.
without the data, some devices can still determine the Voltage, and give a rough estimate of the total capacity or percentage of charge , With the data, (and the correct curcuit to read it) they can get more precise about the percentage of charge left.
when i use a "pack" like this to run a device that does not have a data connection, or thermistor for charge overheat protection, i still use the protection curcuit in the pack to keep it from overcharging or overdischarging.
the ability of the device your running it with to display your charge or run times, will depend on the device. if the device ONLY has the 2 connections, then it can ONLY use the voltage to determine the runtime or percentage of charge, which is usually sufficient when you know about what it means..
so its good to use the pack as a pack, and not direct connect to the cell, unless you can use the protection on the Devices original pack, and just replace the cell (only) into the devices pack.
often a limited pack, upgraded with a extended Cell (only) will not be able to determine all the data on the extended capacity anyways.
sooo, most the time you can just be lucky to use this pack to extend the runtime, and not worry about it reading the percent of charge correctally.
SOME of the time you can replace the cell with the other cell, WITH the original curcuit and get it to calibrate to the extended battery, but its rare, because the DATA curcuits are sometimes SET to a specific capacity of battery.
IF you can buy a real extended battery (with proper data and charge cuircuitry) for the actual device you intend to use it, that is best. but when you gotta do what you gotta do, its best to leave the pack assembled, and use its protection.
after all a RAW cell is much cheaper than a pack, if your going to toss out the protection :-(
its also cheaper to use a raw cell when there Already IS a protection curcuit, you can connect the extended cell item to, to extend the runtime of the device by upgrading the cell, except that sometimes the cuircuit you connect to, wont understand that its larger capacity.