A second casting of True Polymorph would override the initial casting for one of two reasons:
- If the caster had not maintained concentration on the first casting for the hour required to make it last until dispelled, then the first casting of the spell ends before the second begins due to loss of concentration.
- Given that concentration was maintained for the hour then the effects of the second casting of the True Polymorph would then replace that of the first completely as something can only be affected by a single version of the same spell. Though the first casting remains running, the target can only be affected by one of the two spell effects, the latest one.
"Combining Magical Effects" (PHB 205) states:
The effects of the same spell cast multiple times don't combine
Either way there is no "layering" of the spells, only one effects the target and so the target does not have any of the game statistics of a Helmed Horror, that casting of True Polymorph is not in effect at the time the dispel magic occurs.
However for the sake of this argument, let us say there was a magical spell, not True Polymorph, that had transformed a creature into a Helmed Horror and then True Polymorph was cast to turn it into a frog for example, which leaves both spell effects running as they are different spells.
The description of True Polymorph says:
The target's game statistics, including mental ability scores, are replaced by the statistics of the new form. It retains its alignment and personality.
If a creature is True Polymorphed into another creature its game statistics are replaced by the new form regardless of the original spell. The Helmed Horror's spell immunity to Dispel Magic is a game statistic, so if it is True Polymorphed into a frog it loses the Helmed Horror's game statistics and gain the frog's statistics, losing any immunity to Dispel Magic.
So a Dispel Magic cast on the target at that point would dispel all the spell effects it was successful against, the immunity to Dispel Magic that the Helmed Horror form had would have no bearing as it has the game statistics of a frog.
If however the spell that turned the target into a frog was dispelled, but the original True Polymorph was not, then the target would assume the form of a Helmed Horror rather than its original form at that point and would then be immune to Dispel Magic again.