Here in the nominative masculine plural, this perfect participle active, attested only in lexicography, is given by Philoxenus the grammarian (phi,394) in his On -mi Verbs, fr. 442, along with ἐωκώς , as from an Attic dialect form of the perfect indicative active of ἵημι 'let go', otherwise εἷκα . This analysis appears in the definition of ἀνίημι at EM 107.3, Et.Gen. alpha165, Et.Gud. 144. Chantraine (Dictionnaire étymologique 458) takes the forms with omega as from "an old form with the root vowel o-." Forms in alpha such as the headword are not explained, but they may result from back-formations from forms with omega such as ἕωμαι, ἀνέωνται, ἀνεῶσθαι , misinterpreted as being present tenses with crasis of alpha and omega.
The synonyms in Suda also appear at ps.-Zonaras epsilon593.3 and Lex. Segueriana epsilon204.18. Hesychius (epsilon14, cf. 12, 13) has slightly different ones for the nominative singular: κακῶς ἔχων, παρειμένος, ἀναπεπαυμένος, ἀλγῶν 'feeling bad, having been pardoned or let go, having given up or taken a rest (also a euphemism for dying), suffering'. These definitions apply not to the perfect of the simple ἵημι but to that of its compound ἀνίημι , the headword for the etymological analysis deriving from Philoxenus. This compound verb is used intransitively in the meanings attributed to it here (see LSJ link below). Indeed the perfect forms of ἵημι belong almost exclusively to its compounds. To correct the entry, we should supply ἀνεακότες as its headword. This would adequately explain why the headword currently on the entry occurs without the needed rough breathing.