The headword is the aorist active infinitive of the verb thmele/w, I look after; cf. alpha 3450 (gloss), tau 503, tau 504, tau 506, and see generally LSJ s.v. It is evidently extracted from somewhere; the first independent attestation of the headword is at Maximus, Dialexeis 25.1.d2, but an identical entry occurs in Phrynichus (see next note).
[1] The glosses are the same form as the headword, but from the verbs e)pimele/w (I take care of) and fronti/zw (I consider, reflect, take thought), respectively; see generally LSJ s.vv. [e)pimele/omai in respect of the first gloss; LSJ does not register the active voice of this verb, despite its attestation here and already in Fragmenta Comicorum Anonymorum 8 Meineke]. The headword is identically glossed in Phrynichus, Praeparatio sophistica fr. 358.1, Photius' Lexicon, Lexica Segueriana 387.3, and the Synagoge; cf. ps.-Herodian, Partitiones 133.4-5 and ps.-Zonaras 1729. The present active infinitive thmelei=n of the headword verb and the present middle/passive infinitive e)pimelei=sqai of the first gloss's verb occur together at Plato, Laws 953A (web address 1), where the Athenian notes that visitors to the city pursuing the arts are to be looked after and taken care of by temple custodians and priests.