Your players have a great many options, given that you are open to homebrew material:

• They should seek out a Couatl, and undertake a quest to receive it's shielded mind trait
• They could ally themselves with a Flumph and stay very very close to them, so as to benefit from their telepathic shroud. Perhaps, if any of their group is psionic, they could learn to manifest such a shroud themselves.
• They could acquire the aid of a rakshasa, and willingly invoke its curse upon themselves, filling their every thought with horrible images and dreams, and thus discouraging the use of telepathy against them.
• They could start a weekly poker game with an androsphinx and his consort, and so acquire a measure of their inscrutability.

(Basically, any time you're going 'I wanna do a thing/provide my players an opportunity to become able to do a thing' and it's not easily done via spells/magic items, check out the monster manual. Most monster traits are presented in such a way as to make it fictionally reasonable for players to gain access to that trait via some sort of interaction with the monster, be that murdering it and harvesting parts of its corpse or training under it for an extended time period or performing quests for some divine patron or eldritch being or another)

Additionally, in previous editions spell research rules existed, and the ones from AD&D 2e are pretty consistent with the 5e ethos. For some reason (probably game balance-- spell creation in D&D has always been hugely difficult for GMs to properly adjudicate) 5e lacks spell creation rules, but you could certainly import or modify ones from elsewhere. A spell similar to 3.5's False Vision, which has no 5e counterpart yet is not particularly problematic would be a reasonable addition.

I have added False Vision as a 4th level illusion spell with the ritual tag for a wizard in 5e before. I had it require concentration, last up to 24 hours, and require an action to alter the image viewed. I also added a 6th level version that took an hour to cast and didn't require concentration on a round as long as the caster used no movement that round. I changed the material component to a focus component for each. Both worked fine.

Alternatively, a variant on one of the spells that protects or disguises against detection spells could be a decent starting place; they almost do what you want as-is, it would seem.

RAW: No, you can maintain concentration - but you might have to do an extra DC 10 Constitution saving throw to do so

As concentration is a Constitution saving throw, which is not affected by feeblemind, there is no reason why you should not be capable to keep concentrating on the spell.

The rules on concentration specify the following reasons for loosing concentration

• Casting another spell that requires concentration. [...]

• Taking damage. [...]

• Being incapacitated or killed. [...]

The DM might also decide that certain environmental phenomena, such as a wave crashing over you while you're on a storm-tossed ship, require you to succeed on a DC 10 Constitution saving throw to maintain concentration on a spell.

The first 3 reasons do not apply, and the fourth is at your DM's discretion.

Similar situations such as polymorph also do not make you lose concentration. The druid's Wild Shape feature actually explicitly mentions that you can maintain concentration:

You can't cast spells, [...] Transforming doesn’t break your concentration on a spell you’ve already cast, however, or prevent you from taking actions that are part of a spell, such as call lightning, that you’ve already cast.

So, the RAW says that no, you can keep concentrating. Though your DM might force an extra Con save.

As a DM, I would allow you to keep concentrating under the condition that you use the spell the first chance you get.