It's hard to get started

Hello forum!!!

'Since last week, I've been having a problem with the gears (1-5) in my TDI 110PS car. They are very difficult and jerky to engage. When I push the gear knob forward or backward, I feel resistance. It takes a lot of force to get the gear to engage. There are no loud noises or clunking sounds.' The entire process is not speed-dependent, and it doesn't always happen.

A badger chewed through a pair of coolant hoses, and I replaced them. One of the hoses was the one that runs from the engine into the passenger compartment. I disconnected it directly at the engine, and some coolant spilled onto the transmission. Later, I realized that the cover for the clutch was missing, so I can't rule out the possibility that some coolant may have gotten into it. But the clutch isn't slipping.

I've just lubricated all the mechanical components on the gearbox. It has achieved a little bit, but it's still far from being good.

Does anyone have any idea what else it could be?

Thank you in advance.
Regards,
Thomas.