You need to remove the last character in the string then completely redraw the text box. That's about as simple as it'll get. Here's the code I used for an acrostic. Hope it helps!

noLoop();

//adds text to the screen as it is being typed
void keyPressed() {

 //deletes a mistype or typo
 if (key == BACKSPACE) {
   if (typed.length() > 0) {
     typed = typed.substring(0, typed.length()-1);

     fill (0);//changes the fill to the background color

     rect(140, 100, 640, 480);//creates a rectangle fill the above fill
   
fill (255, 255, 255);//changes the fill back to white for the redraw
     redraw();
   }
 }

 //generates the new line if enter is presses
 else if (key == ENTER) {
   typed = typed+"\n";
 }

 //generates the text on screen
 else if (textWidth(typed+key) < width){
   typed = typed+key;
   redraw();
 }

I think you're confused about how processing works, you can't just simply add a text box or something and leave it to be rendered every loop, you have to draw everything to the screen every loop.

Thankfully with clever use of classes, it's not too hard to do.

aah sorry for the misunderstanding, well no its not a standard library, but there is the p5 control library, which is pretty much the accepted standard:

http://www.sojamo.de/libraries/controlP5/