Feeblemind has a duration of instantaneous. However, it also produces an ongoing effect, and the spell's text describes when this effect ends (emphasis added):

At the end of every 30 days, the creature can repeat its saving throw against this spell. If it succeeds on its saving throw, the spell ends.

The spell can also be ended by greater restoration, heal, or wish.

The fact that the text refers to the spell ending, as opposed to just "the effect" or something similar, implies that it produces an ongoing magical spell effect, which can be dispelled using Dispel Magic. However, it has also been argued that any effects that persist beyond a spell's stated duration cannot be considered magical (with the classic example being fires started by a Fireball spell). Applying this rule to Feeblemind, it shouldn't have any ongoing effects since its duration is instantaneous. So, which is it? Are the ongoing effects of Feeblemind considered magical and therefore susceptible to effects like Dispel Magic, or are are they simply the lingering result of the initial shattering of the creature's intellect and personality?

(Note that the final sentence quoted above does not by itself rule out Dispel Magic and other ways of ending the spell. It gives additional options for ending the spell, but it doesn't say these are the only options.)

Feeblemind can't be dispelled

The feeblemind spell has an instantaneous duration which means specifically:

The spell harms, heals, creates, or alters a creature or an object in a way that can't be dispelled, because its magic exists only for an instant.

--- Player's Handbook on Instantaneous duration, p. 203

This is specifically supported by designer intent in a (now unofficial) tweet by Jeremy Crawford.

A spell that has a duration of instantaneous can't be dispelled.

and also this tweet:

The intent is that feeblemind can be ended only by the methods
specified in the spell.

The most likely fix to the ambiguity would to rephrase (or interpret) the later clauses to 'the spell's effect ends'. The game does not always make a distinction between the two terms. Specifically the spell Leomund's secret chest (in the SRD as secret chest) is also instantaneous and includes the paragraph (emphasis mine):

After 60 days, there is a cumulative 5 percent chance per day that the spell's effect ends. This effect ends if you cast this spell again, if the smaller replica chest is destroyed, or if you choose to end the spell as an action. [...]

--- Player's Handbook, p. 254

Here both ending the spell's effect and ending the spell are used to describe the same thing, which is similar to that of feeblemind. Likely if the effect of feeblemind was to be dispellable it's duration would have been listed as 'Until Dispelled' or something similar, like with transmute rock or magic jar.

Yes, Dispel Magic works (but only after a successful Spellcasting Ability Check)

You've quoted the relevant parts of the spell: a creature that succeeds on their latent saving throw "ends the spell". That wouldn't be possible if the effect weren't being maintained by an active "Spell Effect"; therefore, the ongoing effect of Feeblemind must constitute a Spell Effect, dispellable by Dispel Magic. This constitutes a "Specific beats General" exception to the normal rule that Instantaneous Spells must not be dispellable.

The catch, of course, is that Feeblemind, as an 8th level spell, is difficult to remove. Someone trying to dispel it using Dispel Magic would have to either cast Dispel Magic as an 8th level spell, or else pass the Spellcasting Ability check to dispel it; and at a DC of 18, that can be difficult, considering that "Spellcasting Ability check"s don't use the caster's proficiency modifier, and because Dispel Magic does not have material components, certain kinds of magic items (like a +1 Wand, used as an Arcane Focus) would not benefit this check.

_{Other kinds of magic items might count though; check the item description to find out whether it requires that it be actively used as a focus to confer the benefits or not.}

This is why the alternate methods of removing the spell, like Heal, Greater Restoration, or Wish, are a major benefit: they're guaranteed to successfully remove the effect without needing to pass a check, making them under certain circumstances (especially time-constrained circumstances or spell-slot constrained circumstances) much better options for removing this kind of effect. If these options were not listed, then it would be far more difficult to remove this effect.

The Intent is that only the three spells listed are valid to remove the effect

The intent is that feeblemind can be ended only by the methods specified in the spell. #DnD

—Jeremy Crawford, Twitter, 2017-04-03@3:51PM EDT

So at least from the informal perspective of the Lead Rules Designer, the spell should only be removable by those three spells listed above.

I maintain, however, from a Rules-as-Written perspective, that because the spell describes the successful saving throw as ending the spell, it is therefore the case that until errata or a Sage Advice compendium comes out that specifically adjudicates against this, Dispel Magic (and other effects that "end active spells") are valid against Feeblemind.