I am really sorry to hear you had that bad experience but let me do my best to help you.
That part on the processor is a capacitor that manages a specific sector inside the processor. When manufacturing processors, the capacitors can be added in different locations but in a similar way.
If you see that this part is missing and it is visible damage your system can be affected by performance issues when the processor needs to use that specific sector.
It is important to say that there are sectors inside the processor that sometimes are never used due to the functionality or the task running so it is possible you may not see any problem but it is recommendable to replace the unit if it is damaged.