In practice they mean much the same thing, so it is good that they are both allowed, but note that the literal translation is 'frozen' since -te is the past participle ending, equivalent to -ed or -en in English. Recognising this can help you to remember what they mean in two ways. Firstly, you just know to try and think of the correct word with one of these endings, and secondly you will sometimes know the verb - or if you don't before you will learn it. For example when you learn that dùinte means 'closed' then you have learnt that dùin means 'close'. So now you have learnt for free that reòth means 'freeze'.
As far as I can see, all three are acceptable - so yes, let's see. You can generally assume that -te and -ta are interchangeable in past participles even if not listed and even if it breaks the spelling rule, since regardless of how you spell it people will pronounce it as they choose. Adding the i is permitted to obey the spelling rule with -te if you wish. So that makes three. Then add in the option th and you have six.
I am afraid I do not trust Watson, especially when it comes to spelling changes, but Am Faclair Beag basically agrees with this, without actually listing all six variants.
But Mark takes us to the next level, suggesting, in a series of cross references that you can choose dh as a third variant beside th and nothing.
So although he does not list them all, that suggests that there are in fact 9 options:
reòthte, reòdhte, reòte
reòthta, reòdhta, reòta
reòithte, reòidhte, reòite
I think only reòite is common in modern writing though, which is probably the reason that Duo has used this version up to now. But that is a pity as GOC (which is the Bible on these matters) says we should use only reòthta or reòthte. I think that Duo went with what they thought was common practice (which I agree with in this case) but they are slowly going over to GOC, so expect this to change soon - provided someone points it out to them.
Obviously GOC agrees with your logic, even in the face of modern practice.
I sometimes get the impression that GOC hates the removal of silent th and dh and I wonder if this is due to a fear of Gaelic ending up looking like Irish. They have been so ruthless with the pruners that 400-year-old Irish can actually look more like Gaelic than Irish.