How does Iota-Carrageenan achieve an antiviral effect?
Through two different pathways, one relying on a non-specific (innate) response, and another through a reactive oxygen species, the level of NF-kB(**) is amplified, as such a response would have happened as a result of the presence of the virus anyway. 


  In thousands of experiments, carrageenans have been used to
  induce inﬂammation, since inﬂammation is a predictable effect of
  exposure to carrageenan in animal and cell-based models. For the
  most part, these experiments were designed to test the effectiveness of anti-inﬂammatory agents or to study the mediators of inflammation
  
  The innate immune pathway is mediated by toll-like
  receptor (TLR)-4 and B-cell leukemia lymphoma (BCL)10, leading
  to increased Interleukin (IL)-8 secretion by both canonical and noncanonical pathways of NF-kB activation. The ROS-mediated
  pathway of inﬂammation does not involve TLR4-BCL10, but
  requires Hsp27 and IkB-kinase (IKK)b, leading to increased phosphorylation of IkBa, and thereby enabling the nuclear translocation
  of NF-kB.


From the intro to:


  Yang B, Bhattacharyya S, Linhardt R, Tobacman J. (2012) Exposure to common food additive carrageenan leads to reduced sulfatase activity and increase in sulfated glycosaminoglycans in human epithelial cells.  Biochemie, Mar 5,epub ahead of print, doi  


(As an aside, the direct conclusions of this study are that these changes in GAGs may further influence transcription and play a role in determining cell fate, and perhaps may influence cell/cell interactions)


  (**)NF-κB (nuclear factor kappa-light-chain-enhancer of activated B cells) is a protein complex that controls the transcription of DNA. NF-κB is found in almost all animal cell types and is involved in cellular responses to stimuli such as stress, cytokines, free radicals, ultraviolet irradiation, oxidized LDL, and bacterial or viral antigens  wiki