Only if dispel magic is cast at 4th level or higher.

Dispel magic at 3rd level can only end spells:

Any spell of 3rd level or lower on the target ends.

In contrast, dispel magic at 4th level or higher ends spell effects:

When you cast this spell using a spell slot of 4th level or higher, you automatically end the effects of a spell on the target

Once the spell has ended, there is no spell to end, so dispel magic at 3rd will have no effect. But at 4th level or higher, it can end the effects of a spell.

Is it inconsistent? Obviously. But I have ruled it this way in the games I run, and my players have generally preferred it this way: this makes upcasting the spell better, beyond just the "automatically succeed" effect given by upcasting.

Keep in mind, it is still up to the DM to decide if a particular effect is a valid target for dispel magic: When can a magical effect be targeted with the dispel magic spell?

Only if dispel magic is cast at 4th level or higher.

Dispel magic at 3rd level can only end spells:

Any spell of 3rd level or lower on the target ends.

In contrast, dispel magic at 4th level or higher ends spell effects:

When you cast this spell using a spell slot of 4th level or higher, you automatically end the effects of a spell on the target if the spell’s level is equal to or less than the level of the spell slot you used.

Once the spell has ended, there is no spell to end, so dispel magic at 3rd will have no effect. But at 4th level or higher, it can end the effects of a spell.

Is it inconsistent? Obviously, but I have ruled it this way in the games I run, and my players have generally preferred it this way: this makes upcasting the spell better, beyond just the "automatically succeed" effect given by upcasting.

Keep in mind, it is still up to the DM to decide if a particular effect is a valid target for dispel magic: When can a magical effect be targeted with the dispel magic spell?

Only if dispel magic is cast at 4th level or higher.

Dispel magic at 3rd level can only end spells:

Any spell of 3rd level or lower on the target ends.

In contrast, dispel magic at 4th level or higher ends spell effects:

When you cast this spell using a spell slot of 4th level or higher, you automatically end the effects of a spell on the target

Once the spell has ended, there is no spell to end, so dispel magic at 3rd will have no effect. But at 4th level or higher, it can end the effects of a spell.

Keep in mind, it is still up to the DM to decide if a particular effect is a valid target for dispel magic: When can a magical effect be targeted with the dispel magic spell?

Only if dispel magic is cast at 4th level or higher.

Dispel magic at 3rd level can only end spells:

Any spell of 3rd level or lower on the target ends.

In contrast, dispel magic at 4th level or higher ends spell effects:

When you cast this spell using a spell slot of 4th level or higher, you automatically end the effects of a spell on the target

Once the spell has ended, there is no spell to end, so dispel magic at 3rd will have no effect. But at 4th level or higher, it can end the effects of a spell.

Is it inconsistent? Obviously. But I have ruled it this way in the games I run, and my players have generally preferred it this way: this makes upcasting the spell better, beyond just the "automatically succeed" effect given by upcasting.

Keep in mind, it is still up to the DM to decide if a particular effect is a valid target for dispel magic: When can a magical effect be targeted with the dispel magic spell?