Hi,
Usually it is easier to replace the keyboard than try to repair it as you can create more problems than you solve when trying to fix it.
Here is a link to the service manual for your laptop. Scroll to p.65 to view the necessary pre-requisites and then the procedure for removing / replacing the keyboard.
https://download.lenovo.com/ibmdl/pub/pc/pccbbs/mobiles_pdf/t440s_hmm_en_sp40a25360_01.pdf
Keyboards are available online, just search for Lenovo T440s keyboard replacement part to get results.
Here is a link to just one supplier. It is not a recommendation to use the seller, it is just shown to give an idea of the price. There are others that may suit you better. This is for one without the backlight as I wasn't sure what you have.
https://www.amazon.com/Replacement-Keyboard-Thinkpad-Without-Backlight/dp/B00SKERL4G
Hopefully this is of some help.