CortJstr (and someone correct me if I'm wrong): Affectedly precious, but not in an overwrought and fragile way, more like a "yeah we're cute in a way, and we know it and we show it, and we're nice and harmless too, and so, there" sort of thing.
That's what comes to my mind when someone says twee, anyway.
edit to update:
1. Originally: ‘sweet’, dainty, chic. Now only in depreciatory use: affectedly dainty or quaint; over-nice, over-refined, precious, mawkish.
1905 Punch 8 Mar. 178/1, ‘I call him perfectly twee!’ persisted Phyllis. 1917 M. T. Hainsselin Grand Fleet Days xv. 91 Girl: Oh, here's another little gun; isn't it a darling! Isn't it just too twee for words! 1947 E. Hyams William Medium viii. 164 ‘Isn't he twee!’ said Mary, and pinched his cheek. 1956 G. Durrell Drunken Forest x. 193 ‘What twee individuals?’ ‘Those knowledgeable sentimentalists who are forever telling me that it's cruel to lock up the poor wild creatures in little wooden boxes.’ 1962 Observer 25 Mar. 25/3 She has a small and, it must be said, pretty twee cottage. 1967 E. Short Embroidery & Fabric Collage iv. 102 The best of our designers who have abandoned the rather ‘twee’ decorative type of embroidered picture. 1973 G. Robyns Wimbledon xxix. 192 There is+a twee Arcadian outdoor studio complete with white trellis and plastic flowers. 1983 Listener 21 July 33/1 Mike Nichols's thriller-fantasy about dolphins should be as nauseatingly twee as the worst Disney—but it isn't.
I think they meant to say "deprecatory" and not "depreciatory". But it's gone back to being a sort of compliment, IMO-I've never heard it used in a context where I thought it was intended unkindly.
update to my update to correct myself: depreciatory is a word. Who knew?!
Tending to depreciate; of disparaging tendency.
1805 W. Taylor in Ann. Rev. III. 57 This account+is too depretiatory. 1875 Jowett Plate (ed. 2) V. 59, I have a word to say+which may seem to be depreciatory of legislators.
and deprecatory didn't mean what I thought it meant, which was "depreciatory". Instead it means
1. Serving to deprecate; that prays for deliverance from or aversion of evil.
1586 A. Day Eng. Secretary i. (1625) 21 Deprecatorie, in praying for pardon of a thing committed. 1622 Bacon Hen. VII, 190 Bishop Fox+sent many humble and deprecatorie letters to the Scottish King, to appease him. c1630 Donne Serm. 1. 504 All his Prayer+is but Deprecatory, he does but pray that God will forbeare him. 1738 Warburton Div. Legat. I. ii. i. 89 Deprecatory Rites to avert Evil.
2. Expressing a wish or hope that something feared may be averted; deprecating anticipated disapproval.
1704 Swift T. Tub iii. (T.), Before I had performed the due discourses, expostulatory, supplicatory, or deprecatory, with my good lords the criticks. 1838 Lytton Leila i. v, The Israelite did+seem to hear this deprecatory remonstrance. 1871 H. Ainsworth Tower Hill i. viii, ‘Your Grace is mistaken’, observed Cromwell, in a deprecatory tone. 1872 Geo. Eliot Middlem. xvi, ‘Oh’, said Rosamond, with a slight deprecatory laugh, ‘I was only going to say that we sometimes have dancing.’