This is hardened skin due to the pressure of the pen.
I have a similar one on my index finger on the middle knuckle I never had any pressure on that finger, so don't know why it got like that.
You don't say for how long you used the salicylic acid, but you probably didn't continue with the application for long enough. It is something that can grown back as you have experienced by biting the skin off. I cut mine with a pair of scissors and it still grew back as before.
I have an ointment called Diprosalic that was prescribed for my eczema when the skin goes hard, cracks and bleeds. Diprosalic also contains salicylic acid and I have applied that to my hard callus, but I don't apply the ointment for long enough to know if it would work. It probably would if used regularly, because the ointment thins the hardened eczema skin
I did read an article on the web many months ago, and you have to soak the skin, use an emery board to take off the hardened area and apply Vaseline. I never got round to doing it, but you will need to do it for a while until it completely goes. It may grow back hard, I don't know.
Since seeing your post, it spurred me on to do something about my lump.
For the last few days, I have been cutting off the dead skin, but not enough to make it bleed. I have been apply lots of Diprosalic ointment - this was prescribed for me for my dry and splitting dermatitis that I get on some of my fingers from time to time and it does contain soft white paraffin and salicylic acid.
I have been apply the Diprosalic ointment and covering it with a plaster. Every few days I have been rubbing off the dead skin with an emery board and sometimes cutting off the dead skin with scissors.
It is working, but will take some time, may be a few weeks, to look like normal skin on the finger, if it works!
I don't know how my lump appeared and I too have had it for many years - I can't even remember when it started to appear.