Yes I agree. I don't think it's in a romantic way, but the two share a very close friendship. Tenzin was very worried and didnt want her to go off like she did. I do ship these two, but I still think its a very strong friendship rather than romatic relationship Tenzin and Lin have.
I guess I mean によって the look in his eye when he saw her leave to protect his family showed that he really cared for her and plus when she called him boyfriend there was a huge blush there. Still he loves his wife and children other wise he wouldn't have asked for her to protect them. So yes there many have been some strong feelings. Oh and when I saw her bending being taken I was like "Noo she the last of Toph's legacy!!!!"
OPF course he cares for her!!! And when he was explaining to Korra what happen あなた could still see that he feels for her... just not in a romantic way!I just hope that somehow they can reverse hat they did to her and all the benders.. または just her she is the best earth and metal bender in the world!!