No check would be required for a level 13 Warlock.
I think the critical wording for spell scroll is this:
If the spell is on your class’s spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully.
The rule for the scroll make no distinction about the provenance of the caster's ability to cast spells. That is, the caster's spell slots are not the limitation here. It just happens to be that this will usually be the limiting factor.
Warlocks break the rules for spellcasting. They don't get spell slots above level 5 but, for them, that doesn't mean they don't have the ability to cast higher level spells (as a result of Mystic Arcanum).
Since the rule for spell scrolls and casting checks only cares if the caster has the ability to cast spells of the scroll's level, a sufficiently high level Warlock can use spell scrolls that appear on its class list without making an ability check.
Also, as a footnote, I think the word "normally" in the scroll's rules indicates that the ability to cast spells of the requisite level must come from an innate class feature. A character would not "normally" be able to cast such spells if the ability to do so came from some external source such as a magic item or temporary ability that allowed the character to cast level 7+ spells. I would argue that such an item or ability would not satisfy the "normally" requirement because of its transient nature.
Of course, a DM is free to interpret "normally" however s/he likes and, by the time a character is gaining access to items that powerful, the character is likely already high enough level to cast level 7+ spells anyway.
Lore-wise, this makes sense, too. Warlocks have invocations and pacts that center around reading and using eldritch texts and magically understanding languages that they otherwise wouldn't know.
Allowing them to read scrolls as a result of their Mystic Arcanum ability is 100% "on brand" for them.