They don't seem to trust you with it.最好有短语说明.

他们似乎不信任你胜任此事

前面的朋友已对“seem”作了很好的解释，我不想多说了——大辞典里有。我只想试翻一下：
看来他们不相信你胜任此事。

译为：他们在这件事上并不信任你!
seem to be doing sth表示不定式的动作和主句中seem是同一个时态,比如,He seems to be doing his homework. 他好像正在做作业；
seem to do 表示不定式的动作发生在主句动词seem之后,比如It seems to rain. 好像要下雨了. rain的动作,是发生在seem之后的；
seem to have done sth表示不定式的动作发生在主句动词seem之前,比如 she seems to have finished her homework. 她好像做完了她的家庭作业.finish的动作发生在seem之前

他们看起来好像不是很信任你能做这事.
seem to 好起来好像
trust sb with sth 信任某人能做某事。