Do we have to consider the cryptographic properties of the decryption, if we're only using the encryption? Treyfer for example has slower diffusion in decryption. It has full diffusion between words in 2 rounds for encryption and 7 rounds for decryption.

Do we have to consider the (bad) cryptographic properties of the decryption algorithm, if we're only using the encryption algorithm? (For example we are using Treyfer in CTR mode.)

Differently worded: Do we have to consider the bad cryptographic properties of the decryption algorithm if the encryption algorithm can be considered strong as we're usually only using the encryption algorithm?
Diffusion is a requirement for a secure cipher, but it is not by itself sufficient. So even if a certain number of rounds has "full diffusion", it does not mean that the number of rounds is enough. In the case of Treyfer, the decryption direction requires five more rounds for full diffusion, but the suggested number of rounds is much higher at 32. (Even that is not really secure, because the key schedule is broken.)

However, if considering block ciphers more generally the question is whether a block cipher can be secure in the encryption direction without being secure in the decryption direction. The answer is probably yes. For example, Luby and Rackoff showed that a three round Feistel network with a secure PRF is secure against adversaries without access to a decryption oracle, but needed four rounds to prove security against adversaries with such access (which they called strong PRP).

So there seems to be a security difference between a block cipher used only in the forward direction and a block cipher used in both directions.