In this paper, the dirty-tape channel (the white Gaussian channel with causal state interference at the trans-mitter) is revisited by considering a noisy feedback link between the transmitter and receiver. A finite blocklength (FBL) coding scheme is proposed for this model, which is based on the classical Schalkwijk-Kailath (SK) scheme and an existing lattice-based interference canceling scheme. Based on the proposed scheme, an achievable rate for given blocklength and decoding error probability is obtained, and the results of this paper are further illustrated via numerical examples.