First we must examine what it does in a more normal situation.

Pass without Trace provides a Stealth Bonus.

It does not provide cover. It does not provide concealment.

If you use Pass without Trace and try to use Stealth while walking through an area with clear line of sight to alert guards, Pass without Trace doesn't let you make a Stealth roll. Stealth only works on foes that cannot clearly see you.

Now, if the guards are not alert (they have no warning of danger, it is late, or they are looking the other way) you can use Stealth.

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Now, how does this apply with Tremorsense. First, it still grants a +10 bonus to Stealth rolls. If we restrict the spell to only doing this (which is quite reasonable), then walking by a creature with Tremorsense waiting in ambush would be akin to walking by an open guard booth with a guard staring into the corridor. No Stealth bonus helps.

If, however, the guard (umber hulk) is distracted the Stealth can help.

On top of that, 5e spell descriptions have no fluff. So while there is no obvious mechanical effect to "veil of shadows and silence" part of the description, you could argue that this means in marginal cases this might make someone less likely to notice you (when they are relying on hearing or bright light to see you). In other situation they might be more likely to see you (a veil of shadows follows you around as you try to hide in a crowd -- the 30' veil might be easier to see than a halfling between the human's legs!)

It comes down to "is the Umber Hulk attentive", and is the "veil of silence" enough to even permit a Stealth check. This is a classic DM's call. Are there other noises that could mask the adventurer's movement? These adventurers going to be quieter than the Umber Hulk would expect (maybe their footsteps sound like small animals), would that matter?

Both calls -- that the Umber Hulk can see the sneaky adventurers clear as day, and that the Umber Hulk is distractible or distracted and has a chance to miss the quiet adventurers -- are reasonable here.

Tremorsense doesn't negate Pass without Trace

Pass without Trace can help in stealth checks against the perception of a creature with Tremorsense.

Is stealth useful against Tremorsense?

The rules of Tremorsense only serve to state that a creature with that ability perceives the world through ground vibrations. What it doesn't do is give it a supernatural ability to perceive all movement around it automatically.

This means it still needs to pit its perception check against a hidden character's stealth check to perceive them, allowing a stealthy enough character to avoid detection.

(As pointed out by Chris Biasbas, this is backed up by Jeremy Crawford on Twitter)

Does Pass without Trace help against Tremorsense?

Pass without Trace says that "A veil of shadows and silence radiates from you[...]". Silence is the absence of sounds and sounds are vibrations. This means that Pass without Trace magically silences the vibrations creatures affected by the spell create. All of this considered it makes sense to rule that Pass without Trace helps in stealth checks against the perception of a creature with Tremorsense.