Depending upon the contact retention system used in the connector the insertion & removal tools will vary according to type.
Sometimes a standard plastic double ended insertion / removal tool will be recommended. There is often a more durable metal insertion or removal tool available that can be cross-referenced.
Metal tools can be of several designs, in particular: straight slotted, offset slotted, tweezer type, pliers type, impact and pull through for military and proprietary applications. These tools are usually colour coded for size identification.
It is of vital importance to determine the correct one for your application to extend connector life and minimise damage.