MayorAura, Depending on which exact 3DS XL you have, it appears on older model 3DS XL the SD reader looks like it will have to be de-soldered from board and then new reader resoldered to board, this would be best done by some one with micro-soldering skills to prevent further damage to the board and components.
I posted disassembly guides for the newer and older model below which may help. Good luck. I hope this helped you out, if so let me know by pressing the helpful button.
Nintendo 3DS XL 2015 Teardown
Nintendo 3DS XL Motherboard Replacement