Reverse ASCII character map

x86-16 Machine Code, 62 bytes

Hex dump:

BC0100B101B07EBAFE0581EAE00080EA02B402CD1085E4750830E439C5750A30C0B40ACD1084C074094884D275E085D275D831C031E4CD1630E489C5EBC7

Assembly:

mov sp, 0x0001           ; Stack pointer is used as a flag; 0 - Print all characters, 1 - Delete specific character
mov cl, 0x01             ; Number of characters to print per interrupt call

printString:
  mov al, 0x7E           ; Last character to print
  mov dx, 0x05FE         ; Row: 0x05, Collumn: 0xFE
  printRow:
    sub dx, 0x00E0       ; Decrement row number + 2 extra characters
    printChar:
      sub dl, 0x02       ; Decrement collumn index + 1 space
      mov ah, 0x02       ; Prepare for interrupt call, 0x02 - Set cursor position
      int 0x10           ; BIOS interrupt

      test sp, sp        ; Are we printing all characters or removing specific character
      jnz print          ; In first case just print it and go on
      xor ah, ah         ; Otherwise reset the upper byte of ax (shorter than "and ax, 0x00FF")
      cmp bp, ax         ; Is the current character same as the input character
      jne after          ; If no, continue searching
      xor al, al         ; If yes, remove it

      print:
        mov ah, 0x0A     ; Prepare for print
        int 0x10         ; Print

      test al, al        ; If we found target character
      jz loop            ; then stop searching

      after:
        dec ax           ; Shorter than "dec, al"
        test dl, dl      ; Is it the last character in the row
        jnz printChar    ; If no, continue searching
    test dx, dx          ; Is it last char
    jnz printRow         ; If no, go to next row

loop:
  xor ax, ax             ; Remove "ah" cache
  xor sp, sp             ; Reset sp (it will never become 1 again)
  int 0x16               ; BIOS interrupt for reading keyboard input
  xor ah, ah             ; Again reset "ah", because BIOS may change it
  mov bp, ax             ; Save it in stack base pointer
  jmp printString        ; Remove the character from the list

SOGL V0.12, 23 bytes

] ~Δ8«n"5αx2⁰³⁄¹‘→č@ŗ░T

Try it Here!

Takes input in the input box. I hope that it isn't too big of an issue that characters can be deleted :p

Explanation:

]                   do.. while (popping (which makes the stack not blow up luckily :D))
  ~Δ                push the ascii characters (range("~"))
    8«n             split into lines of length 16
       "...‘        push "inputs.value" (could be 2 bytes less if my dictionary contained the word "inputs". I even added "input", but only now realise that the input box is id=inputs :/)
            →       evaluate as JavaScript, then push the result
             č      chop into characters
              @ŗ    replace each of the characters in the array with space
                ░   clear the output
                 T  output without popping (so do..while continues looping)

C++ (Visual C++), 253 (@Step Hen) 261 bytes

#include<cstdlib>
#include<iostream>
#include<conio.h>
int main(){char a[0x5E];for(int i=0;i<0x5E;i++)a[i]=(char)(i+0x20);while(true){system("cls");for(int i=0;i<0x5E;i++)if(i&&!(i%16))printf("\n%c ",a[i]);else printf("%c ",a[i]);a[_getch()-0x20]=' ';}}