Grep that tolerates mismatches to subset .fastq

I am working with bash on a linux cluster. I am trying to extract reads from a .fastq file if they contain a match to a queried sequence. Below is an example .fastq file containing three reads.

$ cat example.fastq

@SRR1111111.1 1/1
CTGGANAAGTGAAATAATATAAATTTTTCCACTATTGAATAAAAGCAACTTAAATTTTCTAAGTCG
+
AAAAA#EEEEEEEEEEEEEEEEEEEEEEEAEEEEEEEEEEEEEEEEEEEEEEEEEA<AAEEEEE<6
@SRR1111111.2 2/1
CTATANTATTCTATATTTATTCTAGATAAAAGCATTCTATATTTAGCATATGTCTAGCAAAAAAAA
+
AAAAA#EE6EEEEEEEEEEEEAAEEAEEEEEEEEEEEE/EAE/EAE/EA/EAEAAAE//EEAEAA6
@SRR1111111.3 3/1
CTATANTATTGAAATAATAATGTAGATAAAACTATTGAATAACAGCAACTTAAATTTTCAATAAGA
+
AAAAA#EE6EEEEEEEEEEEEAAEEAEEEEEEEEEEEE/EAE/EAE/EA/EAEAAAE//EEAEAA6

I would like to extract reads containing the sequence GAAATAATA. I can perform this extraction using grep as shown in the following command.

$ grep -F -B 1 -A 2 "GAAATAATA" example.fastq > MATCH.fastq

$ cat MATCH.fastq

@SRR1111111.1 1/1
CTGGANAAGTGAAATAATATAAATTTTTCCACTATTGAATAAAAGCAACTTAAATTTTCTAAGTCG
+
AAAAA#EEEEEEEEEEEEEEEEEEEEEEEAEEEEEEEEEEEEEEEEEEEEEEEEEA<AAEEEEE<6
@SRR1111111.3 3/1
CTATANTATTGAAATAATAATGTAGATAAAACTATTGAATAACAGCAACTTAAATTTTCAATAAGA
+
AAAAA#EE6EEEEEEEEEEEEAAEEAEEEEEEEEEEEE/EAE/EAE/EA/EAEAAAE//EEAEAA6

However, this strategy does not tolerate any mismatches. For example, a read containing the sequence GAAATGATA will be ignored. I need this extraction to tolerate one mismatch at any position in the queried sequence. So my question is how can I achieve this? Is there a sequence alignment package available with similar functionality to grep? Are there any fastq subsetting packages available that perform this type of operation? One note is that speed is very important. Thanks for your guidance.

Here is a solution using agrep to get the record numbers of matches and an awk that prints out those records with some context (due to missing -Aand -B in agrep):

$ agrep -1 -n  "GAAATGATA" file | 
  awk -F: 'NR==FNR{for(i=($1-1);i<=($1+2);i++)a[i];next}FNR in a' - file

Output:

@SRR1111111.1 1/1
CTGGANAAGTGAAATAATATAAATTTTTCCACTATTGAATAAAAGCAACTTAAATTTTCTAAGTCG
+
AAAAA#EEEEEEEEEEEEEEEEEEEEEEEAEEEEEEEEEEEEEEEEEEEEEEEEEA<AAEEEEE<6
@SRR1111111.3 3/1
CTATANTATTGAAATAATAATGTAGATAAAACTATTGAATAACAGCAACTTAAATTTTCAATAAGA
+
AAAAA#EE6EEEEEEEEEEEEAAEEAEEEEEEEEEEEE/EAE/EAE/EA/EAEAAAE//EEAEAA6