If a creature has already moved on its turn, does the Glamour Bard's Mantle of Inspiration allow it to move again?

Question

College of Glamour bards gain the Mantle of Inspiration feature at 3rd level (Xanathar's Guide to Everything, p. 14):

As a bonus action, you can expend one use of your Bardic Inspiration to grant yourself a wondrous appearance. When you do so, choose a number of creatures you can see and that can see you within 60 feet of you, up to a number equal to your Charisma modifier (minimum of one). Each of them gains 5 temporary hit points. When a creature gains these temporary hit points, it can immediately use its reaction to move up to its speed, without provoking opportunity attacks.

If a character has already completed their turn and has moved their maximum move speed, but are then affected by Mantle of Inspiration, will they

A) move their speed once again?
or
B) remain where they are?

If a character has already completed their turn but has moved less than their maximum move speed, but are then affected by Mantle of Inspiration, will they

A) move their maximum speed and their remaining from their turn?
or
B) move only their maximum speed?
or
C) move only their remaining speed?

Answer 1

Each creature can move up to its maximum speed

Barring speed-reducing effects (like the slow spell), there is no difference between your "current" speed and your "maximum" speed. Therefore, each creature may use a reaction to move up to its speed, no matter how much they moved during their turn. For more evidence, let's look how a single creature with multiple different speeds is handled (PHB, p. 190):

Using Different Speeds

If you have more than one speed, such as your walking speed and a flying speed, you can switch back and forth between your speeds during your move. Whenever you switch, subtract the distance you've already moved from the new speed. The result determines how much farther you can move. [...]

For example, if you have a speed of 30 and a flying speed of 60 ... you could fly 20 feet, then walk 10 feet, and then leap into the air to fly 30 feet or more.

If your speed was "used up" during your turn, then the above example would work differently. You would fly 20 feet (reducing your fly speed to 40), then walk 10 feet. You would then subtract 30 (the distance already moved) from your fly speed (reduced to 40 by moving) and only be able to move 10 feet. Thus, we can conclude that speed is not "used up" during your turn.

Answer 2

Speed vs. movement

The term speed is defined roughly here in the basic rules:

Every character and monster has a speed, which is the distance in feet that the character or monster can walk in 1 round.

For player characters, that speed is generally defined by their race, though class features may modify it or grant them other types of movement speeds (e.g. a climb speed or fly speed).

The rules on movement and position in combat state:

On your turn, you can move a distance up to your speed. You can use as much or as little of your speed as you like on your turn, following the rules here.

Your movement can include jumping, climbing, and swimming. These different modes of movement can be combined with walking, or they can constitute your entire move. However you're moving, you deduct the distance of each part of your move from your speed until it is used up or until you are done moving.

In addition to their ability to move up to their speed, characters can also take the Dash action to increase their movement for that turn:

When you take the Dash action, you gain extra movement for the current turn. The increase equals your speed, after applying any modifiers. With a speed of 30 feet, for example, you can move up to 60 feet on your turn if you dash.

Any increase or decrease to your speed changes this additional movement by the same amount. If your speed of 30 feet is reduced to 15 feet, for instance, you can move up to 30 feet this turn if you dash.

Thus, characters have a general "movement" pool on their turn that is dependent on their speed. However, this only applies to the regular movement they can use as part of their turn. Normally, characters do not have any ability to move outside of their turn.

Mantle of Inspiration is unaffected by any previous movement by the character

The Glamour bard's Mantle of Inspiration feature lets them expend a Bardic Inspiration die to give themselves and a number of other creatures temp HP. It adds:

When a creature gains these temporary hit points, it can immediately use its reaction to move up to its speed, without provoking opportunity attacks.

This ability is not affected in any way by the creature's prior movement on any turn. It simply lets them use their reaction to move immediately (as soon as they get the temp HP). The distance they can move is limited only by their speed - not by its movement on a previous turn.