As Russell Borogove and Bob Jacobsen write, indeed Triton wil raise tides on Neptune. But they won't be like the tides people envision here on Earth.
Complex modeling of the vertical structure of Neptune (behind a paywall, but the abstract says enough) by researchers like Sushil Atreya suggests there is no liquid water ocean at Neptune, but instead an "ionic ocean" of water with dissolved ammonia very deep in the atmosphere, deep enough to have pressures in the thousands of bars. At those depths the temperatures are so high (2,000-5,000 K) they are well above the 647 K critical temperature of water, so liquid water doesn't exist. Instead you have a supercritical fluid that is dense like a liquid but compressible like a gas, with other characteristics (like chemical reactivity) that you don't find in the liquid or gaseous state.
Notably, at Neptune (and at other giant planets) there is no discontinuous surface where above it is one state and below it is another. Here on Earth we're quite accustomed to such a discontinuous (at least on human scales) surface, like the surface of our oceans: above that surface is a gas, our atmosphere, and below it is a liquid. Instead, at Neptune the water density and content of other species grades gradually as you go down. So you can't see a discontinuous surface rising and falling with respect to its surroundings, like an ocean level at a shoreline.
Here on Earth we see the tides at the boundaries of liquids and solids—shorelines of continents and islands. The response of the liquid in our oceans to tidal forces is larger than the response of the solid part of Earth. Seeing that difference with human eyes is only possible when you have solid Earth extending above the ocean's level. Were Earth's lithosphere (the solid part) completely smooth, i.e. no topography, and the oceans a uniformly deep layer above that, someone floating on that ocean wouldn't detect the tidal rise and fall without instruments that go far, far beyond human senses.
Similarly, you couldn't detect the tidal response at Neptune. It's made even more difficult to detect by the absence of a discontinuous surface as a reference.
By the way, this reference (that I found while searching for Sushil's) attributes the same paper to the wrong Atreya!