The string as you've shown in your (I assume) Data::Dumper output is the two characters $ and t, and {'$t'} is the correct way to access the hash entry whose key is that two-character string. The string '\$t' consists of three characters, \, $ and t, because backslashes in single-quoted strings work differently than in double-quoted strings - see Quote and Quote like Operators. You don't need to escape $ in a single-quoted string.
I am trying to get the Feed Updated value, this gives me the current time, and not the time value of 2019-07-19
Sorry, this doesn't make sense to me. Based on what you've shown here, there is no way that accessing the key differently would give you a different value. I suspect the data structure actually contains the value it's showing you. If you continue to have trouble, please provide a Short, Self-Contained, Correct Example that reproduces the isse.