Any kind of adhesive mount is always going to be iffy. That's what it really comes down to. It might hold forever, or it may fall off in an hour, a day, a month, a year, or even ten years. And there's always the chance that the adhesive will, in some way, discolor and/or damage the tile or grout.

Depending on your setup, there's an option you can consider that will hold that wood bar in place securely without damaging the tile, but it's a little bit more involved. If you have cabinets right above there, you could get two more pieces of wood (you could even buy another one of those same pieces and cut it in half), screw the ends to the ends of that board, and screw the other ends to the bottom of the cabinets. So, the knife holder would sit against the backsplash, but it would actually be hanging down from the cabinets above.

If you wanted to do something maybe fancier but more involved, you could even get something like a one-foot-square wood cutting board (any kind you like--you could even have it say "MrHL7's Kitchen" in fancy script), screw it to the bottom of the cabinet so it's hanging down in front of the backsplash, then mount the knife holder near the bottom of that cutting board.