Some trophoblast excreting digestive enzymes in implantation
I have no idea what is meant by 'the simplest trophoblast'. I did, however, find this review, pointing to a role of proteases in the implantation process:


  Salamonsen L.A. Salamonsen and Nie, G. (2002) Proteases at the Endometrial–Trophoblast Interface: Their Role in Implantation. Reviews in Endocrine and Metabolic Disorders, 3:133-143


which discusses the roles in implantation of three classes of proteases : matrix metalloproteinases, serine proteinases and cystein proteinases. The reference to 'trypsin-like' presumably relates to the serine proteases. The review reports the results of a number of gene knockout experiments in mice in which genes for individual proteases have been disrupted which indicate that no single enzyme is identified as being essential.

Referring to 


  Afonso S et al (1997) The expression and function of cystatin C and cathepsin B and cathepsin L during mouse embryo implantation and placentation. Development 124:3415-3425.


the authors of the review state that:


  [they] demonstrated that cysteine proteases play a critical role in implantation. Cathepsin B mRNA was expressed by mouse trophoblast throughout the invasive period (days 5.5±10.5) while the proteins for cathepsins B and L were localized to the mature invasive trophoblast giant cells; activity of these enzymes was also demonstrated. Cathepsin L was also present within the stroma particularly in the lateral decidualizing zone. Cystatin C, the major inhibitor of cathepsins, was shown to be a major product of the adjacent decidualizing stroma close to the embryo, suggesting a restraining role. After the completion of placental trophoblast invasion (day 11.5) the trophoblast cells express high levels of cystatin C, probably in association with a switch from an invasive cell type to one providing nutrients to the conceptus [35]. In addition, treatment of pregnant mice with E-64, a synthetic cysteine protease inhibitor, resulted in failure of implantation and normal uterine decidualization.