Considering Suggestion isn't technically a charm, but that those who are immune to charms are immune to its effects, does it logically follow that a Warlock could turn suggestion back on the caster? Would the Warlock get to instead tell the caster what they want them to do, would they do what the enemy initially tried to suggest to the caster, or would they just have the charmed condition?
This question/answer pair talks about Fey Ancestry and what happens if you are charmed, but not of suggestion, nor how a Warlock could retaliate to this spell being cast on them.
BEGUILING DEFENSES
Beginning at 10th level, your patron teaches you how to
turn the mind-affecting magic of your enemies against
them. You are immune to being charmed, and when
another creature attempts to charm you, you can use
your reaction to attempt to turn the charm back on
that creature. The creature must succeed on a Wisdom
saving throw against your warlock spell save DC or
be charmed by you for 1 minute or until the creature takes any damage.
Best Answer
As far as the rules are concerned, no. You've already made the distinction - Beguiling Defenses only works against being Charmed, and Suggestion doesn't Charm. You are immune to Suggestion, since it specifies that
You can, of course, talk to your DM and ask them to rule that Beguiling Defenses works fully against Suggestion. There's definitely a case for it, considering the flavour:
And the fact that Beguiling Defenses makes you immune to Suggestion, which suggests (pun intended) that it should work, even though it technically doesn't.